LSTM_Time_Series_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LSTM for Time Series Forecasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "from pandas import Series\n",
    "from pandas import concat\n",
    "from pandas import read_csv\n",
    "from pandas import datetime\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import LSTM\n",
    "from math import sqrt\n",
    "from matplotlib import pyplot\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# date-time parsing function for loading the dataset\n",
    "def parser(x):\n",
    "\treturn datetime.strptime(x, '%Y-%m')\n",
    "\n",
    "# frame a sequence as a supervised learning problem\n",
    "def timeseries_to_supervised(data, lag=1):\n",
    "\tdf = DataFrame(data)\n",
    "\tcolumns = [df.shift(i) for i in range(1, lag+1)]\n",
    "\tcolumns.append(df)\n",
    "\tdf = concat(columns, axis=1)\n",
    "\tdf.fillna(0, inplace=True)\n",
    "\treturn df\n",
    "\n",
    "# create a differenced series\n",
    "def difference(dataset, interval=1):\n",
    "\tdiff = list()\n",
    "\tfor i in range(interval, len(dataset)):\n",
    "\t\tvalue = dataset[i] - dataset[i - interval]\n",
    "\t\tdiff.append(value)\n",
    "\treturn Series(diff)\n",
    "\n",
    "# invert differenced value\n",
    "def inverse_difference(history, yhat, interval=1):\n",
    "\treturn yhat + history[-interval]\n",
    "\n",
    "# scale train and test data to [-1, 1]\n",
    "def scale(train, test):\n",
    "\t# fit scaler\n",
    "\tscaler = MinMaxScaler(feature_range=(-1, 1))\n",
    "\tscaler = scaler.fit(train)\n",
    "\t# transform train\n",
    "\ttrain = train.reshape(train.shape[0], train.shape[1])\n",
    "\ttrain_scaled = scaler.transform(train)\n",
    "\t# transform test\n",
    "\ttest = test.reshape(test.shape[0], test.shape[1])\n",
    "\ttest_scaled = scaler.transform(test)\n",
    "\treturn scaler, train_scaled, test_scaled\n",
    "\n",
    "# inverse scaling for a forecasted value\n",
    "def invert_scale(scaler, X, value):\n",
    "\tnew_row = [x for x in X] + [value]\n",
    "\tarray = numpy.array(new_row)\n",
    "\tarray = array.reshape(1, len(array))\n",
    "\tinverted = scaler.inverse_transform(array)\n",
    "\treturn inverted[0, -1]\n",
    "\n",
    "# fit an LSTM network to training data\n",
    "def fit_lstm(train, batch_size, nb_epoch, neurons):\n",
    "\tX, y = train[:, 0:-1], train[:, -1]\n",
    "\tX = X.reshape(X.shape[0], 1, X.shape[1])\n",
    "\tmodel = Sequential()\n",
    "\tmodel.add(LSTM(neurons, batch_input_shape=(batch_size, X.shape[1], X.shape[2]), stateful=True))\n",
    "\tmodel.add(Dense(1))\n",
    "\tmodel.compile(loss='mean_squared_error', optimizer='adam')\n",
    "\tfor i in range(nb_epoch):\n",
    "\t\tmodel.fit(X, y, epochs=1, batch_size=batch_size, verbose=0, shuffle=False)\n",
    "\t\tmodel.reset_states()\n",
    "\treturn model\n",
    "\n",
    "# make a one-step forecast\n",
    "def forecast_lstm(model, batch_size, X):\n",
    "\tX = X.reshape(1, 1, len(X))\n",
    "\tyhat = model.predict(X, batch_size=batch_size)\n",
    "\treturn yhat[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# load dataset\n",
    "series = read_csv('monthly-sunspot-number-zurich-17.csv', header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Month\n",
       "1749-01-01    58.0\n",
       "1749-02-01    62.6\n",
       "1749-03-01    70.0\n",
       "1749-04-01    55.7\n",
       "1749-05-01    85.0\n",
       "Name: Monthly sunspot number, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# transform data to be stationary\n",
    "raw_values = series.values\n",
    "diff_values = difference(raw_values, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# transform data to be supervised learning\n",
    "supervised = timeseries_to_supervised(diff_values, 1)\n",
    "supervised_values = supervised.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.    4.6]\n",
      " [  4.6   7.4]\n",
      " [  7.4 -14.3]\n",
      " ..., \n",
      " [-21.5   5.5]\n",
      " [  5.5 -22.5]\n",
      " [-22.5   0.1]]\n"
     ]
    }
   ],
   "source": [
    "print(supervised_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2819, 2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "supervised_values.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# split data into train and test-sets\n",
    "train, test = supervised_values[0:-2184], supervised_values[-2184:]\n",
    "\n",
    "# transform the scale of the data\n",
    "scaler, train_scaled, test_scaled = scale(train, test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# fit the model\n",
    "lstm_model = fit_lstm(train_scaled, 1, 1500, 1)\n",
    "# forecast the entire training dataset to build up state for forecasting\n",
    "train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)\n",
    "lstm_model.predict(train_reshaped, batch_size=1)\n",
    "\n",
    "# walk-forward validation on the test data\n",
    "predictions = list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Month=1, Predicted=46.472594, Expected=47.800000\n",
      "Month=2, Predicted=49.372589, Expected=47.000000\n",
      "Month=3, Predicted=49.361521, Expected=40.800000\n",
      "Month=4, Predicted=44.792625, Expected=42.000000\n",
      "Month=5, Predicted=43.904100, Expected=44.000000\n",
      "Month=6, Predicted=45.047410, Expected=46.000000\n",
      "Month=7, Predicted=46.995104, Expected=48.000000\n",
      "Month=8, Predicted=49.078269, Expected=50.000000\n",
      "Month=9, Predicted=51.119771, Expected=51.800000\n",
      "Month=10, Predicted=52.998331, Expected=38.500000\n",
      "Month=11, Predicted=43.882495, Expected=34.500000\n",
      "Month=12, Predicted=38.531931, Expected=50.000000\n",
      "Month=13, Predicted=45.166105, Expected=50.000000\n",
      "Month=14, Predicted=50.063066, Expected=50.800000\n",
      "Month=15, Predicted=52.408051, Expected=29.500000\n",
      "Month=16, Predicted=36.020880, Expected=25.000000\n",
      "Month=17, Predicted=29.412769, Expected=44.300000\n",
      "Month=18, Predicted=37.259062, Expected=36.000000\n",
      "Month=19, Predicted=36.894922, Expected=48.300000\n",
      "Month=20, Predicted=45.101548, Expected=34.100000\n",
      "Month=21, Predicted=38.234638, Expected=45.300000\n",
      "Month=22, Predicted=42.864109, Expected=54.300000\n",
      "Month=23, Predicted=52.004865, Expected=51.000000\n",
      "Month=24, Predicted=53.360363, Expected=48.000000\n",
      "Month=25, Predicted=51.217094, Expected=45.300000\n",
      "Month=26, Predicted=48.412368, Expected=48.300000\n",
      "Month=27, Predicted=49.278465, Expected=48.000000\n",
      "Month=28, Predicted=49.708690, Expected=50.600000\n",
      "Month=29, Predicted=51.560255, Expected=33.400000\n",
      "Month=30, Predicted=39.284895, Expected=34.800000\n",
      "Month=31, Predicted=37.064058, Expected=29.800000\n",
      "Month=32, Predicted=33.163866, Expected=43.100000\n",
      "Month=33, Predicted=39.428100, Expected=53.000000\n",
      "Month=34, Predicted=50.392400, Expected=62.300000\n",
      "Month=35, Predicted=61.017288, Expected=61.000000\n",
      "Month=36, Predicted=63.273059, Expected=60.000000\n",
      "Month=37, Predicted=62.597229, Expected=61.000000\n",
      "Month=38, Predicted=62.732983, Expected=44.100000\n",
      "Month=39, Predicted=50.158406, Expected=51.400000\n",
      "Month=40, Predicted=51.287788, Expected=37.500000\n",
      "Month=41, Predicted=42.361984, Expected=39.000000\n",
      "Month=42, Predicted=40.918071, Expected=40.500000\n",
      "Month=43, Predicted=41.657851, Expected=37.600000\n",
      "Month=44, Predicted=40.229881, Expected=42.700000\n",
      "Month=45, Predicted=42.833841, Expected=44.400000\n",
      "Month=46, Predicted=45.317699, Expected=29.400000\n",
      "Month=47, Predicted=35.057235, Expected=41.000000\n",
      "Month=48, Predicted=38.757654, Expected=38.300000\n",
      "Month=49, Predicted=39.734657, Expected=39.000000\n",
      "Month=50, Predicted=40.673349, Expected=29.600000\n",
      "Month=51, Predicted=34.231715, Expected=32.700000\n",
      "Month=52, Predicted=34.035043, Expected=27.700000\n",
      "Month=53, Predicted=30.885200, Expected=26.400000\n",
      "Month=54, Predicted=28.986117, Expected=25.600000\n",
      "Month=55, Predicted=27.837670, Expected=30.000000\n",
      "Month=56, Predicted=30.262028, Expected=26.300000\n",
      "Month=57, Predicted=28.975184, Expected=24.000000\n",
      "Month=58, Predicted=26.880194, Expected=27.000000\n",
      "Month=59, Predicted=27.963317, Expected=25.000000\n",
      "Month=60, Predicted=27.283250, Expected=24.000000\n",
      "Month=61, Predicted=26.339670, Expected=12.000000\n",
      "Month=62, Predicted=17.350595, Expected=12.200000\n",
      "Month=63, Predicted=14.799549, Expected=9.600000\n",
      "Month=64, Predicted=12.338927, Expected=23.800000\n",
      "Month=65, Predicted=19.589819, Expected=10.000000\n",
      "Month=66, Predicted=13.464574, Expected=12.000000\n",
      "Month=67, Predicted=13.397229, Expected=12.700000\n",
      "Month=68, Predicted=14.120592, Expected=12.000000\n",
      "Month=69, Predicted=14.032980, Expected=5.700000\n",
      "Month=70, Predicted=9.597085, Expected=8.000000\n",
      "Month=71, Predicted=9.465211, Expected=2.600000\n",
      "Month=72, Predicted=5.974004, Expected=0.000000\n",
      "Month=73, Predicted=3.064345, Expected=0.000000\n",
      "Month=74, Predicted=2.061653, Expected=4.500000\n",
      "Month=75, Predicted=4.659044, Expected=0.000000\n",
      "Month=76, Predicted=2.885962, Expected=12.300000\n",
      "Month=77, Predicted=9.264398, Expected=13.500000\n",
      "Month=78, Predicted=13.929651, Expected=13.500000\n",
      "Month=79, Predicted=15.413747, Expected=6.700000\n",
      "Month=80, Predicted=10.809661, Expected=8.000000\n",
      "Month=81, Predicted=9.923808, Expected=11.700000\n",
      "Month=82, Predicted=12.105981, Expected=4.700000\n",
      "Month=83, Predicted=8.329339, Expected=10.500000\n",
      "Month=84, Predicted=10.531252, Expected=12.300000\n",
      "Month=85, Predicted=13.075190, Expected=7.200000\n",
      "Month=86, Predicted=10.521399, Expected=9.200000\n",
      "Month=87, Predicted=10.721072, Expected=0.900000\n",
      "Month=88, Predicted=5.118912, Expected=2.500000\n",
      "Month=89, Predicted=4.292608, Expected=2.000000\n",
      "Month=90, Predicted=3.894775, Expected=7.700000\n",
      "Month=91, Predicted=7.413303, Expected=0.300000\n",
      "Month=92, Predicted=3.870854, Expected=0.200000\n",
      "Month=93, Predicted=2.529940, Expected=0.400000\n",
      "Month=94, Predicted=2.229463, Expected=0.000000\n",
      "Month=95, Predicted=1.969260, Expected=0.000000\n",
      "Month=96, Predicted=1.899429, Expected=0.000000\n",
      "Month=97, Predicted=1.887005, Expected=0.000000\n",
      "Month=98, Predicted=1.889105, Expected=0.000000\n",
      "Month=99, Predicted=1.891422, Expected=0.000000\n",
      "Month=100, Predicted=1.892235, Expected=0.000000\n",
      "Month=101, Predicted=1.892345, Expected=0.000000\n",
      "Month=102, Predicted=1.892306, Expected=0.000000\n",
      "Month=103, Predicted=1.892276, Expected=0.000000\n",
      "Month=104, Predicted=1.892267, Expected=0.000000\n",
      "Month=105, Predicted=1.892266, Expected=0.000000\n",
      "Month=106, Predicted=1.892266, Expected=0.000000\n",
      "Month=107, Predicted=1.892267, Expected=0.000000\n",
      "Month=108, Predicted=1.892267, Expected=0.000000\n",
      "Month=109, Predicted=1.892267, Expected=0.000000\n",
      "Month=110, Predicted=1.892267, Expected=0.000000\n",
      "Month=111, Predicted=1.892267, Expected=0.000000\n",
      "Month=112, Predicted=1.892267, Expected=0.000000\n",
      "Month=113, Predicted=1.892267, Expected=0.000000\n",
      "Month=114, Predicted=1.892267, Expected=0.000000\n",
      "Month=115, Predicted=1.892267, Expected=6.600000\n",
      "Month=116, Predicted=5.978583, Expected=0.000000\n",
      "Month=117, Predicted=3.284305, Expected=2.400000\n",
      "Month=118, Predicted=3.775099, Expected=6.100000\n",
      "Month=119, Predicted=6.474575, Expected=0.800000\n",
      "Month=120, Predicted=4.013976, Expected=1.100000\n",
      "Month=121, Predicted=3.215653, Expected=11.300000\n",
      "Month=122, Predicted=9.033614, Expected=1.900000\n",
      "Month=123, Predicted=5.318322, Expected=0.700000\n",
      "Month=124, Predicted=3.375879, Expected=0.000000\n",
      "Month=125, Predicted=2.229766, Expected=1.000000\n",
      "Month=126, Predicted=2.545754, Expected=1.300000\n",
      "Month=127, Predicted=2.982766, Expected=0.500000\n",
      "Month=128, Predicted=2.632518, Expected=15.600000\n",
      "Month=129, Predicted=11.027076, Expected=5.200000\n",
      "Month=130, Predicted=7.979813, Expected=3.900000\n",
      "Month=131, Predicted=6.459584, Expected=7.900000\n",
      "Month=132, Predicted=8.399419, Expected=10.100000\n",
      "Month=133, Predicted=10.898969, Expected=0.000000\n",
      "Month=134, Predicted=4.589592, Expected=10.300000\n",
      "Month=135, Predicted=8.468253, Expected=1.900000\n",
      "Month=136, Predicted=5.044856, Expected=16.600000\n",
      "Month=137, Predicted=12.299153, Expected=5.500000\n",
      "Month=138, Predicted=8.418712, Expected=11.200000\n",
      "Month=139, Predicted=11.103075, Expected=18.300000\n",
      "Month=140, Predicted=17.137682, Expected=8.400000\n",
      "Month=141, Predicted=12.448385, Expected=15.300000\n",
      "Month=142, Predicted=14.988163, Expected=27.800000\n",
      "Month=143, Predicted=24.213717, Expected=16.700000\n",
      "Month=144, Predicted=20.215798, Expected=14.300000\n",
      "Month=145, Predicted=17.416523, Expected=22.200000\n",
      "Month=146, Predicted=21.120446, Expected=12.000000\n",
      "Month=147, Predicted=15.906876, Expected=5.700000\n",
      "Month=148, Predicted=10.030992, Expected=23.800000\n",
      "Month=149, Predicted=17.614830, Expected=5.800000\n",
      "Month=150, Predicted=8.996604, Expected=14.900000\n",
      "Month=151, Predicted=12.944326, Expected=18.500000\n",
      "Month=152, Predicted=18.212903, Expected=2.300000\n",
      "Month=153, Predicted=7.812671, Expected=8.100000\n",
      "Month=154, Predicted=8.514866, Expected=19.300000\n",
      "Month=155, Predicted=16.161342, Expected=14.500000\n",
      "Month=156, Predicted=16.702715, Expected=20.100000\n",
      "Month=157, Predicted=20.173659, Expected=19.200000\n",
      "Month=158, Predicted=21.053049, Expected=32.200000\n",
      "Month=159, Predicted=28.814945, Expected=26.200000\n",
      "Month=160, Predicted=28.554092, Expected=31.600000\n",
      "Month=161, Predicted=31.737452, Expected=9.800000\n",
      "Month=162, Predicted=15.912404, Expected=55.900000\n",
      "Month=163, Predicted=28.316829, Expected=35.500000\n",
      "Month=164, Predicted=25.354911, Expected=47.200000\n",
      "Month=165, Predicted=42.092895, Expected=31.500000\n",
      "Month=166, Predicted=35.733895, Expected=33.500000\n",
      "Month=167, Predicted=35.226781, Expected=37.200000\n",
      "Month=168, Predicted=37.568928, Expected=65.000000\n",
      "Month=169, Predicted=53.195216, Expected=26.300000\n",
      "Month=170, Predicted=31.459410, Expected=68.800000\n",
      "Month=171, Predicted=42.581353, Expected=73.700000\n",
      "Month=172, Predicted=55.989349, Expected=58.800000\n",
      "Month=173, Predicted=56.136413, Expected=44.300000\n",
      "Month=174, Predicted=48.516695, Expected=43.600000\n",
      "Month=175, Predicted=46.163516, Expected=38.800000\n",
      "Month=176, Predicted=42.251912, Expected=23.200000\n",
      "Month=177, Predicted=29.514093, Expected=47.800000\n",
      "Month=178, Predicted=38.051640, Expected=56.400000\n",
      "Month=179, Predicted=52.650106, Expected=38.100000\n",
      "Month=180, Predicted=43.095879, Expected=29.900000\n",
      "Month=181, Predicted=34.994531, Expected=36.400000\n",
      "Month=182, Predicted=36.337923, Expected=57.900000\n",
      "Month=183, Predicted=49.515233, Expected=96.200000\n",
      "Month=184, Predicted=85.547159, Expected=26.400000\n",
      "Month=185, Predicted=34.320654, Expected=21.200000\n",
      "Month=186, Predicted=25.774209, Expected=40.000000\n",
      "Month=187, Predicted=33.031508, Expected=50.000000\n",
      "Month=188, Predicted=46.692793, Expected=45.000000\n",
      "Month=189, Predicted=47.881223, Expected=36.700000\n",
      "Month=190, Predicted=41.562657, Expected=25.600000\n",
      "Month=191, Predicted=31.402210, Expected=28.900000\n",
      "Month=192, Predicted=30.444818, Expected=28.400000\n",
      "Month=193, Predicted=30.142676, Expected=34.900000\n",
      "Month=194, Predicted=34.248508, Expected=22.400000\n",
      "Month=195, Predicted=27.037163, Expected=25.400000\n",
      "Month=196, Predicted=26.767326, Expected=34.500000\n",
      "Month=197, Predicted=32.505483, Expected=53.100000\n",
      "Month=198, Predicted=47.084068, Expected=36.400000\n",
      "Month=199, Predicted=40.123201, Expected=28.000000\n",
      "Month=200, Predicted=32.802282, Expected=31.500000\n",
      "Month=201, Predicted=32.646755, Expected=26.100000\n",
      "Month=202, Predicted=29.325462, Expected=31.700000\n",
      "Month=203, Predicted=31.675855, Expected=10.900000\n",
      "Month=204, Predicted=16.805784, Expected=25.800000\n",
      "Month=205, Predicted=21.541930, Expected=32.500000\n",
      "Month=206, Predicted=30.438506, Expected=20.700000\n",
      "Month=207, Predicted=25.052892, Expected=3.700000\n",
      "Month=208, Predicted=10.529274, Expected=20.200000\n",
      "Month=209, Predicted=15.814419, Expected=19.600000\n",
      "Month=210, Predicted=19.704017, Expected=35.000000\n",
      "Month=211, Predicted=30.634179, Expected=31.400000\n",
      "Month=212, Predicted=33.172623, Expected=26.100000\n",
      "Month=213, Predicted=29.900982, Expected=14.900000\n",
      "Month=214, Predicted=20.486229, Expected=27.500000\n",
      "Month=215, Predicted=24.702473, Expected=25.100000\n",
      "Month=216, Predicted=26.282705, Expected=30.600000\n",
      "Month=217, Predicted=30.495020, Expected=19.200000\n",
      "Month=218, Predicted=23.837144, Expected=26.600000\n",
      "Month=219, Predicted=26.140053, Expected=4.500000\n",
      "Month=220, Predicted=10.377092, Expected=19.400000\n",
      "Month=221, Predicted=15.020816, Expected=29.300000\n",
      "Month=222, Predicted=26.105075, Expected=10.800000\n",
      "Month=223, Predicted=15.788214, Expected=20.600000\n",
      "Month=224, Predicted=18.947704, Expected=25.900000\n",
      "Month=225, Predicted=24.940441, Expected=5.200000\n",
      "Month=226, Predicted=10.989678, Expected=9.000000\n",
      "Month=227, Predicted=10.166787, Expected=7.900000\n",
      "Month=228, Predicted=9.708329, Expected=9.700000\n",
      "Month=229, Predicted=10.901334, Expected=21.500000\n",
      "Month=230, Predicted=18.502297, Expected=4.300000\n",
      "Month=231, Predicted=8.909212, Expected=5.700000\n",
      "Month=232, Predicted=7.537636, Expected=9.200000\n",
      "Month=233, Predicted=9.585470, Expected=1.700000\n",
      "Month=234, Predicted=5.442409, Expected=1.800000\n",
      "Month=235, Predicted=4.071096, Expected=2.500000\n",
      "Month=236, Predicted=4.122261, Expected=4.800000\n",
      "Month=237, Predicted=5.770935, Expected=4.400000\n",
      "Month=238, Predicted=6.250571, Expected=18.800000\n",
      "Month=239, Predicted=14.639748, Expected=4.400000\n",
      "Month=240, Predicted=8.099758, Expected=0.000000\n",
      "Month=241, Predicted=3.659155, Expected=0.000000\n",
      "Month=242, Predicted=2.178814, Expected=0.900000\n",
      "Month=243, Predicted=2.406676, Expected=16.100000\n",
      "Month=244, Predicted=11.368565, Expected=13.500000\n",
      "Month=245, Predicted=14.636890, Expected=1.500000\n",
      "Month=246, Predicted=6.750370, Expected=5.600000\n",
      "Month=247, Predicted=6.742176, Expected=7.900000\n",
      "Month=248, Predicted=8.605153, Expected=2.100000\n",
      "Month=249, Predicted=5.513407, Expected=0.000000\n",
      "Month=250, Predicted=2.960118, Expected=0.400000\n",
      "Month=251, Predicted=2.305897, Expected=0.000000\n",
      "Month=252, Predicted=1.951247, Expected=0.000000\n",
      "Month=253, Predicted=1.882792, Expected=0.000000\n",
      "Month=254, Predicted=1.881474, Expected=0.000000\n",
      "Month=255, Predicted=1.888447, Expected=0.600000\n",
      "Month=256, Predicted=2.283506, Expected=0.000000\n",
      "Month=257, Predicted=2.054322, Expected=0.000000\n",
      "Month=258, Predicted=1.936659, Expected=0.000000\n",
      "Month=259, Predicted=1.894457, Expected=0.500000\n",
      "Month=260, Predicted=2.215017, Expected=0.000000\n",
      "Month=261, Predicted=2.025585, Expected=0.000000\n",
      "Month=262, Predicted=1.928807, Expected=0.000000\n",
      "Month=263, Predicted=1.894072, Expected=0.000000\n",
      "Month=264, Predicted=1.889052, Expected=20.400000\n",
      "Month=265, Predicted=12.883621, Expected=21.600000\n",
      "Month=266, Predicted=20.980069, Expected=10.800000\n",
      "Month=267, Predicted=15.494864, Expected=0.000000\n",
      "Month=268, Predicted=5.747200, Expected=19.400000\n",
      "Month=269, Predicted=12.811884, Expected=2.800000\n",
      "Month=270, Predicted=5.439831, Expected=0.000000\n",
      "Month=271, Predicted=2.686702, Expected=0.000000\n",
      "Month=272, Predicted=1.939219, Expected=1.400000\n",
      "Month=273, Predicted=2.728451, Expected=20.500000\n",
      "Month=274, Predicted=13.726862, Expected=25.200000\n",
      "Month=275, Predicted=24.144289, Expected=0.000000\n",
      "Month=276, Predicted=6.413864, Expected=0.800000\n",
      "Month=277, Predicted=3.305123, Expected=5.000000\n",
      "Month=278, Predicted=5.132263, Expected=15.500000\n",
      "Month=279, Predicted=12.875739, Expected=22.400000\n",
      "Month=280, Predicted=21.418062, Expected=3.800000\n",
      "Month=281, Predicted=9.474261, Expected=15.400000\n",
      "Month=282, Predicted=13.064868, Expected=15.400000\n",
      "Month=283, Predicted=15.990719, Expected=30.900000\n",
      "Month=284, Predicted=26.354373, Expected=25.400000\n",
      "Month=285, Predicted=27.439378, Expected=15.700000\n",
      "Month=286, Predicted=20.633027, Expected=15.600000\n",
      "Month=287, Predicted=18.247922, Expected=11.700000\n",
      "Month=288, Predicted=14.894297, Expected=22.000000\n",
      "Month=289, Predicted=19.804965, Expected=17.700000\n",
      "Month=290, Predicted=19.802752, Expected=18.200000\n",
      "Month=291, Predicted=20.087488, Expected=36.700000\n",
      "Month=292, Predicted=30.298552, Expected=24.000000\n",
      "Month=293, Predicted=26.404339, Expected=32.400000\n",
      "Month=294, Predicted=31.002514, Expected=37.100000\n",
      "Month=295, Predicted=36.720539, Expected=52.500000\n",
      "Month=296, Predicted=48.213012, Expected=39.600000\n",
      "Month=297, Predicted=43.284501, Expected=18.900000\n",
      "Month=298, Predicted=25.811248, Expected=50.600000\n",
      "Month=299, Predicted=35.884479, Expected=39.500000\n",
      "Month=300, Predicted=35.867597, Expected=68.100000\n",
      "Month=301, Predicted=56.862094, Expected=34.600000\n",
      "Month=302, Predicted=39.367335, Expected=47.400000\n",
      "Month=303, Predicted=43.437624, Expected=57.800000\n",
      "Month=304, Predicted=54.480144, Expected=46.000000\n",
      "Month=305, Predicted=49.969395, Expected=56.300000\n",
      "Month=306, Predicted=54.461402, Expected=56.700000\n",
      "Month=307, Predicted=57.527792, Expected=42.900000\n",
      "Month=308, Predicted=48.354304, Expected=53.700000\n",
      "Month=309, Predicted=51.829931, Expected=49.600000\n",
      "Month=310, Predicted=51.561440, Expected=57.200000\n",
      "Month=311, Predicted=56.256475, Expected=48.200000\n",
      "Month=312, Predicted=51.990464, Expected=46.100000\n",
      "Month=313, Predicted=49.160775, Expected=52.800000\n",
      "Month=314, Predicted=52.217008, Expected=64.400000\n",
      "Month=315, Predicted=61.272698, Expected=65.000000\n",
      "Month=316, Predicted=65.994809, Expected=61.100000\n",
      "Month=317, Predicted=64.374358, Expected=89.100000\n",
      "Month=318, Predicted=76.855066, Expected=98.000000\n",
      "Month=319, Predicted=94.243916, Expected=54.300000\n",
      "Month=320, Predicted=61.901325, Expected=76.400000\n",
      "Month=321, Predicted=67.655140, Expected=50.400000\n",
      "Month=322, Predicted=53.670340, Expected=54.700000\n",
      "Month=323, Predicted=54.318207, Expected=57.000000\n",
      "Month=324, Predicted=57.280643, Expected=46.600000\n",
      "Month=325, Predicted=51.110047, Expected=43.000000\n",
      "Month=326, Predicted=46.698443, Expected=49.400000\n",
      "Month=327, Predicted=49.039555, Expected=72.300000\n",
      "Month=328, Predicted=63.352636, Expected=95.000000\n",
      "Month=329, Predicted=90.070316, Expected=67.500000\n",
      "Month=330, Predicted=73.573564, Expected=73.900000\n",
      "Month=331, Predicted=74.029193, Expected=90.800000\n",
      "Month=332, Predicted=84.735051, Expected=78.300000\n",
      "Month=333, Predicted=80.940033, Expected=52.800000\n",
      "Month=334, Predicted=59.806571, Expected=57.200000\n",
      "Month=335, Predicted=58.481117, Expected=67.600000\n",
      "Month=336, Predicted=64.751486, Expected=56.500000\n",
      "Month=337, Predicted=60.077099, Expected=52.200000\n",
      "Month=338, Predicted=55.878652, Expected=72.100000\n",
      "Month=339, Predicted=64.777923, Expected=84.600000\n",
      "Month=340, Predicted=80.924361, Expected=107.100000\n",
      "Month=341, Predicted=101.528172, Expected=66.300000\n",
      "Month=342, Predicted=73.400559, Expected=65.100000\n",
      "Month=343, Predicted=68.124016, Expected=43.900000\n",
      "Month=344, Predicted=50.521959, Expected=50.700000\n",
      "Month=345, Predicted=50.830921, Expected=62.100000\n",
      "Month=346, Predicted=58.680621, Expected=84.400000\n",
      "Month=347, Predicted=77.157527, Expected=81.200000\n",
      "Month=348, Predicted=82.585281, Expected=82.100000\n",
      "Month=349, Predicted=84.134429, Expected=47.500000\n",
      "Month=350, Predicted=55.060907, Expected=50.100000\n",
      "Month=351, Predicted=52.130751, Expected=93.400000\n",
      "Month=352, Predicted=68.458671, Expected=54.600000\n",
      "Month=353, Predicted=53.954641, Expected=38.100000\n",
      "Month=354, Predicted=42.547126, Expected=33.400000\n",
      "Month=355, Predicted=37.064277, Expected=45.200000\n",
      "Month=356, Predicted=42.166984, Expected=54.900000\n",
      "Month=357, Predicted=52.298571, Expected=37.900000\n",
      "Month=358, Predicted=42.860481, Expected=46.200000\n",
      "Month=359, Predicted=45.312119, Expected=43.500000\n",
      "Month=360, Predicted=45.366601, Expected=28.900000\n",
      "Month=361, Predicted=34.709628, Expected=30.900000\n",
      "Month=362, Predicted=32.980986, Expected=55.500000\n",
      "Month=363, Predicted=45.014214, Expected=55.100000\n",
      "Month=364, Predicted=53.381195, Expected=26.900000\n",
      "Month=365, Predicted=33.400318, Expected=41.300000\n",
      "Month=366, Predicted=37.340431, Expected=26.700000\n",
      "Month=367, Predicted=30.039512, Expected=13.900000\n",
      "Month=368, Predicted=19.542837, Expected=8.900000\n",
      "Month=369, Predicted=13.254449, Expected=8.200000\n",
      "Month=370, Predicted=10.755570, Expected=21.100000\n",
      "Month=371, Predicted=17.426881, Expected=14.300000\n",
      "Month=372, Predicted=16.578499, Expected=27.500000\n",
      "Month=373, Predicted=24.050068, Expected=11.300000\n",
      "Month=374, Predicted=15.535928, Expected=14.900000\n",
      "Month=375, Predicted=15.790464, Expected=11.800000\n",
      "Month=376, Predicted=14.289054, Expected=2.800000\n",
      "Month=377, Predicted=7.494401, Expected=12.900000\n",
      "Month=378, Predicted=11.129740, Expected=1.000000\n",
      "Month=379, Predicted=4.937148, Expected=7.000000\n",
      "Month=380, Predicted=6.914123, Expected=5.700000\n",
      "Month=381, Predicted=7.427643, Expected=11.600000\n",
      "Month=382, Predicted=11.321744, Expected=7.500000\n",
      "Month=383, Predicted=10.230752, Expected=5.900000\n",
      "Month=384, Predicted=8.598143, Expected=9.900000\n",
      "Month=385, Predicted=10.442391, Expected=4.900000\n",
      "Month=386, Predicted=7.993535, Expected=18.100000\n",
      "Month=387, Predicted=14.597125, Expected=3.900000\n",
      "Month=388, Predicted=7.721807, Expected=1.400000\n",
      "Month=389, Predicted=4.472321, Expected=8.800000\n",
      "Month=390, Predicted=7.870120, Expected=7.800000\n",
      "Month=391, Predicted=9.294845, Expected=8.700000\n",
      "Month=392, Predicted=10.331923, Expected=4.000000\n",
      "Month=393, Predicted=7.375407, Expected=11.500000\n",
      "Month=394, Predicted=10.736376, Expected=24.800000\n",
      "Month=395, Predicted=20.909131, Expected=30.500000\n",
      "Month=396, Predicted=29.956001, Expected=34.500000\n",
      "Month=397, Predicted=35.227695, Expected=7.500000\n",
      "Month=398, Predicted=14.342209, Expected=24.500000\n",
      "Month=399, Predicted=19.291651, Expected=19.700000\n",
      "Month=400, Predicted=20.409396, Expected=61.500000\n",
      "Month=401, Predicted=39.658156, Expected=43.600000\n",
      "Month=402, Predicted=38.752426, Expected=33.200000\n",
      "Month=403, Predicted=35.564140, Expected=59.800000\n",
      "Month=404, Predicted=48.313159, Expected=59.000000\n",
      "Month=405, Predicted=56.823735, Expected=100.800000\n",
      "Month=406, Predicted=82.337586, Expected=95.200000\n",
      "Month=407, Predicted=90.079826, Expected=100.000000\n",
      "Month=408, Predicted=99.717592, Expected=77.500000\n",
      "Month=409, Predicted=83.843413, Expected=88.600000\n",
      "Month=410, Predicted=86.653501, Expected=107.600000\n",
      "Month=411, Predicted=100.577969, Expected=98.100000\n",
      "Month=412, Predicted=100.078383, Expected=142.900000\n",
      "Month=413, Predicted=118.065302, Expected=111.400000\n",
      "Month=414, Predicted=108.730215, Expected=124.700000\n",
      "Month=415, Predicted=119.429620, Expected=116.700000\n",
      "Month=416, Predicted=119.026699, Expected=107.800000\n",
      "Month=417, Predicted=112.571217, Expected=95.100000\n",
      "Month=418, Predicted=101.210600, Expected=137.400000\n",
      "Month=419, Predicted=113.772824, Expected=120.900000\n",
      "Month=420, Predicted=112.583065, Expected=206.200000\n",
      "Month=421, Predicted=162.796219, Expected=188.000000\n",
      "Month=422, Predicted=171.699397, Expected=175.600000\n",
      "Month=423, Predicted=173.208360, Expected=134.600000\n",
      "Month=424, Predicted=142.065121, Expected=138.200000\n",
      "Month=425, Predicted=139.309527, Expected=111.300000\n",
      "Month=426, Predicted=117.944146, Expected=158.000000\n",
      "Month=427, Predicted=129.407931, Expected=162.800000\n",
      "Month=428, Predicted=141.695241, Expected=134.000000\n",
      "Month=429, Predicted=133.109475, Expected=96.300000\n",
      "Month=430, Predicted=103.600847, Expected=123.700000\n",
      "Month=431, Predicted=110.675952, Expected=107.000000\n",
      "Month=432, Predicted=105.712885, Expected=129.800000\n",
      "Month=433, Predicted=120.280741, Expected=144.900000\n",
      "Month=434, Predicted=141.785593, Expected=84.800000\n",
      "Month=435, Predicted=92.720654, Expected=140.800000\n",
      "Month=436, Predicted=103.785990, Expected=126.600000\n",
      "Month=437, Predicted=103.279372, Expected=137.600000\n",
      "Month=438, Predicted=124.166002, Expected=94.500000\n",
      "Month=439, Predicted=100.260920, Expected=108.200000\n",
      "Month=440, Predicted=103.622620, Expected=78.800000\n",
      "Month=441, Predicted=84.247761, Expected=73.600000\n",
      "Month=442, Predicted=77.386987, Expected=90.800000\n",
      "Month=443, Predicted=84.680477, Expected=77.400000\n",
      "Month=444, Predicted=79.750828, Expected=79.800000\n",
      "Month=445, Predicted=80.746108, Expected=107.600000\n",
      "Month=446, Predicted=95.526475, Expected=102.500000\n",
      "Month=447, Predicted=100.756289, Expected=77.700000\n",
      "Month=448, Predicted=83.765362, Expected=61.800000\n",
      "Month=449, Predicted=68.633690, Expected=53.800000\n",
      "Month=450, Predicted=59.375849, Expected=54.600000\n",
      "Month=451, Predicted=57.001856, Expected=84.700000\n",
      "Month=452, Predicted=70.457047, Expected=131.200000\n",
      "Month=453, Predicted=123.962074, Expected=132.700000\n",
      "Month=454, Predicted=136.079715, Expected=90.800000\n",
      "Month=455, Predicted=98.720654, Expected=68.800000\n",
      "Month=456, Predicted=76.565069, Expected=63.600000\n",
      "Month=457, Predicted=68.964367, Expected=81.200000\n",
      "Month=458, Predicted=75.566416, Expected=87.700000\n",
      "Month=459, Predicted=85.619042, Expected=55.500000\n",
      "Month=460, Predicted=62.302994, Expected=65.900000\n",
      "Month=461, Predicted=64.015048, Expected=69.200000\n",
      "Month=462, Predicted=68.580419, Expected=48.500000\n",
      "Month=463, Predicted=54.348035, Expected=60.700000\n",
      "Month=464, Predicted=57.944783, Expected=57.800000\n",
      "Month=465, Predicted=59.052198, Expected=74.000000\n",
      "Month=466, Predicted=68.992206, Expected=49.800000\n",
      "Month=467, Predicted=54.740619, Expected=54.300000\n",
      "Month=468, Predicted=54.688113, Expected=53.700000\n",
      "Month=469, Predicted=55.136671, Expected=24.000000\n",
      "Month=470, Predicted=31.105515, Expected=29.900000\n",
      "Month=471, Predicted=30.386967, Expected=29.700000\n",
      "Month=472, Predicted=30.897424, Expected=42.600000\n",
      "Month=473, Predicted=39.037169, Expected=67.400000\n",
      "Month=474, Predicted=58.980381, Expected=55.700000\n",
      "Month=475, Predicted=57.838058, Expected=30.800000\n",
      "Month=476, Predicted=37.718098, Expected=39.300000\n",
      "Month=477, Predicted=38.753637, Expected=35.100000\n",
      "Month=478, Predicted=37.337107, Expected=28.500000\n",
      "Month=479, Predicted=32.502342, Expected=19.800000\n",
      "Month=480, Predicted=24.780575, Expected=38.800000\n",
      "Month=481, Predicted=32.204511, Expected=20.400000\n",
      "Month=482, Predicted=23.435465, Expected=22.100000\n",
      "Month=483, Predicted=23.230044, Expected=21.700000\n",
      "Month=484, Predicted=23.396790, Expected=26.900000\n",
      "Month=485, Predicted=26.825289, Expected=24.900000\n",
      "Month=486, Predicted=27.050281, Expected=20.500000\n",
      "Month=487, Predicted=23.948386, Expected=12.600000\n",
      "Month=488, Predicted=17.258478, Expected=26.500000\n",
      "Month=489, Predicted=22.756249, Expected=18.500000\n",
      "Month=490, Predicted=20.828511, Expected=38.100000\n",
      "Month=491, Predicted=31.094176, Expected=40.500000\n",
      "Month=492, Predicted=39.714272, Expected=17.600000\n",
      "Month=493, Predicted=23.821406, Expected=13.300000\n",
      "Month=494, Predicted=17.524135, Expected=3.500000\n",
      "Month=495, Predicted=8.703236, Expected=8.300000\n",
      "Month=496, Predicted=8.992064, Expected=8.800000\n",
      "Month=497, Predicted=10.011184, Expected=21.100000\n",
      "Month=498, Predicted=17.885496, Expected=10.500000\n",
      "Month=499, Predicted=13.944107, Expected=9.500000\n",
      "Month=500, Predicted=12.120575, Expected=11.800000\n",
      "Month=501, Predicted=12.935554, Expected=4.200000\n",
      "Month=502, Predicted=8.147968, Expected=5.300000\n",
      "Month=503, Predicted=7.230948, Expected=19.100000\n",
      "Month=504, Predicted=14.983461, Expected=12.700000\n",
      "Month=505, Predicted=14.818064, Expected=9.400000\n",
      "Month=506, Predicted=12.557613, Expected=14.700000\n",
      "Month=507, Predicted=14.847710, Expected=13.600000\n",
      "Month=508, Predicted=15.403970, Expected=20.800000\n",
      "Month=509, Predicted=20.005127, Expected=12.000000\n",
      "Month=510, Predicted=15.798934, Expected=3.700000\n",
      "Month=511, Predicted=8.578511, Expected=21.200000\n",
      "Month=512, Predicted=15.497188, Expected=23.900000\n",
      "Month=513, Predicted=22.914275, Expected=6.900000\n",
      "Month=514, Predicted=12.385958, Expected=21.500000\n",
      "Month=515, Predicted=17.588884, Expected=10.700000\n",
      "Month=516, Predicted=13.492757, Expected=21.600000\n",
      "Month=517, Predicted=19.082503, Expected=25.700000\n",
      "Month=518, Predicted=25.302526, Expected=43.600000\n",
      "Month=519, Predicted=38.208610, Expected=43.300000\n",
      "Month=520, Predicted=44.178104, Expected=56.900000\n",
      "Month=521, Predicted=53.755754, Expected=47.800000\n",
      "Month=522, Predicted=51.117476, Expected=31.100000\n",
      "Month=523, Predicted=37.670857, Expected=30.600000\n",
      "Month=524, Predicted=33.881867, Expected=32.300000\n",
      "Month=525, Predicted=33.676065, Expected=29.600000\n",
      "Month=526, Predicted=32.135520, Expected=40.700000\n",
      "Month=527, Predicted=38.121092, Expected=39.400000\n",
      "Month=528, Predicted=40.675209, Expected=59.700000\n",
      "Month=529, Predicted=52.665220, Expected=38.700000\n",
      "Month=530, Predicted=42.439548, Expected=51.000000\n",
      "Month=531, Predicted=47.548075, Expected=63.900000\n",
      "Month=532, Predicted=59.990951, Expected=69.200000\n",
      "Month=533, Predicted=69.133693, Expected=59.900000\n",
      "Month=534, Predicted=64.465745, Expected=65.100000\n",
      "Month=535, Predicted=65.715281, Expected=46.500000\n",
      "Month=536, Predicted=52.332229, Expected=54.800000\n",
      "Month=537, Predicted=54.020603, Expected=107.100000\n",
      "Month=538, Predicted=76.293185, Expected=55.900000\n",
      "Month=539, Predicted=56.481143, Expected=60.400000\n",
      "Month=540, Predicted=58.427278, Expected=65.500000\n",
      "Month=541, Predicted=64.507991, Expected=62.600000\n",
      "Month=542, Predicted=65.020346, Expected=44.900000\n",
      "Month=543, Predicted=51.332340, Expected=85.700000\n",
      "Month=544, Predicted=63.483815, Expected=44.700000\n",
      "Month=545, Predicted=45.623485, Expected=75.400000\n",
      "Month=546, Predicted=58.185312, Expected=85.300000\n",
      "Month=547, Predicted=78.662767, Expected=52.200000\n",
      "Month=548, Predicted=58.350627, Expected=140.600000\n",
      "Month=549, Predicted=73.916001, Expected=161.200000\n",
      "Month=550, Predicted=79.641685, Expected=180.400000\n",
      "Month=551, Predicted=95.129661, Expected=138.900000\n",
      "Month=552, Predicted=82.056623, Expected=109.600000\n",
      "Month=553, Predicted=73.098299, Expected=159.100000\n",
      "Month=554, Predicted=142.148975, Expected=111.800000\n",
      "Month=555, Predicted=118.185975, Expected=108.900000\n",
      "Month=556, Predicted=112.534777, Expected=107.100000\n",
      "Month=557, Predicted=109.736012, Expected=102.200000\n",
      "Month=558, Predicted=105.689293, Expected=123.800000\n",
      "Month=559, Predicted=115.420023, Expected=139.200000\n",
      "Month=560, Predicted=134.780421, Expected=132.500000\n",
      "Month=561, Predicted=135.758028, Expected=100.300000\n",
      "Month=562, Predicted=107.893460, Expected=132.400000\n",
      "Month=563, Predicted=117.357793, Expected=114.600000\n",
      "Month=564, Predicted=112.627804, Expected=159.900000\n",
      "Month=565, Predicted=135.444819, Expected=156.700000\n",
      "Month=566, Predicted=145.244498, Expected=131.700000\n",
      "Month=567, Predicted=134.551593, Expected=96.500000\n",
      "Month=568, Predicted=104.132709, Expected=102.500000\n",
      "Month=569, Predicted=102.969836, Expected=80.600000\n",
      "Month=570, Predicted=86.577542, Expected=81.200000\n",
      "Month=571, Predicted=83.519058, Expected=78.000000\n",
      "Month=572, Predicted=80.755751, Expected=61.300000\n",
      "Month=573, Predicted=67.604140, Expected=93.700000\n",
      "Month=574, Predicted=78.272979, Expected=71.500000\n",
      "Month=575, Predicted=70.776557, Expected=99.700000\n",
      "Month=576, Predicted=86.496160, Expected=97.000000\n",
      "Month=577, Predicted=94.474083, Expected=78.000000\n",
      "Month=578, Predicted=83.268584, Expected=89.400000\n",
      "Month=579, Predicted=87.014723, Expected=82.600000\n",
      "Month=580, Predicted=85.076222, Expected=44.100000\n",
      "Month=581, Predicted=51.926431, Expected=61.600000\n",
      "Month=582, Predicted=56.212903, Expected=70.000000\n",
      "Month=583, Predicted=66.829084, Expected=39.100000\n",
      "Month=584, Predicted=45.535092, Expected=61.600000\n",
      "Month=585, Predicted=52.448244, Expected=86.200000\n",
      "Month=586, Predicted=78.134401, Expected=71.000000\n",
      "Month=587, Predicted=74.399565, Expected=54.800000\n",
      "Month=588, Predicted=61.321779, Expected=60.000000\n",
      "Month=589, Predicted=61.074162, Expected=75.500000\n",
      "Month=590, Predicted=70.256586, Expected=105.400000\n",
      "Month=591, Predicted=95.263945, Expected=64.600000\n",
      "Month=592, Predicted=70.855325, Expected=56.500000\n",
      "Month=593, Predicted=61.395151, Expected=62.600000\n",
      "Month=594, Predicted=62.440545, Expected=63.200000\n",
      "Month=595, Predicted=64.146486, Expected=36.100000\n",
      "Month=596, Predicted=42.914553, Expected=57.400000\n",
      "Month=597, Predicted=49.433511, Expected=67.900000\n",
      "Month=598, Predicted=63.850978, Expected=62.500000\n",
      "Month=599, Predicted=65.282756, Expected=50.900000\n",
      "Month=600, Predicted=56.509303, Expected=71.400000\n",
      "Month=601, Predicted=64.194853, Expected=68.400000\n",
      "Month=602, Predicted=68.107032, Expected=67.500000\n",
      "Month=603, Predicted=69.504259, Expected=61.200000\n",
      "Month=604, Predicted=65.214158, Expected=65.400000\n",
      "Month=605, Predicted=66.176490, Expected=54.900000\n",
      "Month=606, Predicted=59.407267, Expected=46.900000\n",
      "Month=607, Predicted=51.819142, Expected=42.000000\n",
      "Month=608, Predicted=46.123886, Expected=39.700000\n",
      "Month=609, Predicted=42.756570, Expected=37.500000\n",
      "Month=610, Predicted=40.257571, Expected=67.300000\n",
      "Month=611, Predicted=53.451571, Expected=54.300000\n",
      "Month=612, Predicted=52.547592, Expected=45.400000\n",
      "Month=613, Predicted=48.723746, Expected=41.100000\n",
      "Month=614, Predicted=44.714963, Expected=42.900000\n",
      "Month=615, Predicted=44.441187, Expected=37.700000\n",
      "Month=616, Predicted=41.040911, Expected=47.600000\n",
      "Month=617, Predicted=45.680855, Expected=34.700000\n",
      "Month=618, Predicted=38.887077, Expected=40.000000\n",
      "Month=619, Predicted=40.276788, Expected=45.900000\n",
      "Month=620, Predicted=45.123093, Expected=50.400000\n",
      "Month=621, Predicted=50.368005, Expected=33.500000\n",
      "Month=622, Predicted=39.169489, Expected=42.300000\n",
      "Month=623, Predicted=41.381437, Expected=28.800000\n",
      "Month=624, Predicted=33.319213, Expected=23.400000\n",
      "Month=625, Predicted=27.554025, Expected=15.400000\n",
      "Month=626, Predicted=20.172779, Expected=20.000000\n",
      "Month=627, Predicted=20.664625, Expected=20.700000\n",
      "Month=628, Predicted=21.866246, Expected=26.400000\n",
      "Month=629, Predicted=26.074874, Expected=24.000000\n",
      "Month=630, Predicted=26.265949, Expected=21.100000\n",
      "Month=631, Predicted=24.138713, Expected=18.700000\n",
      "Month=632, Predicted=21.649560, Expected=15.800000\n",
      "Month=633, Predicted=18.832918, Expected=22.400000\n",
      "Month=634, Predicted=21.873834, Expected=12.700000\n",
      "Month=635, Predicted=16.670961, Expected=28.200000\n",
      "Month=636, Predicted=23.544211, Expected=21.400000\n",
      "Month=637, Predicted=23.190788, Expected=12.300000\n",
      "Month=638, Predicted=16.924584, Expected=11.400000\n",
      "Month=639, Predicted=14.226950, Expected=17.400000\n",
      "Month=640, Predicted=17.014032, Expected=4.400000\n",
      "Month=641, Predicted=9.139167, Expected=9.100000\n",
      "Month=642, Predicted=9.767880, Expected=5.300000\n",
      "Month=643, Predicted=7.936209, Expected=0.400000\n",
      "Month=644, Predicted=4.019101, Expected=3.100000\n",
      "Month=645, Predicted=4.321480, Expected=0.000000\n",
      "Month=646, Predicted=2.637313, Expected=9.700000\n",
      "Month=647, Predicted=7.804839, Expected=4.300000\n",
      "Month=648, Predicted=6.851506, Expected=3.100000\n",
      "Month=649, Predicted=5.643470, Expected=0.500000\n",
      "Month=650, Predicted=3.385721, Expected=4.900000\n",
      "Month=651, Predicted=5.300556, Expected=0.400000\n",
      "Month=652, Predicted=3.298880, Expected=6.500000\n",
      "Month=653, Predicted=6.282952, Expected=0.000000\n",
      "Month=654, Predicted=3.300572, Expected=5.000000\n",
      "Month=655, Predicted=5.319727, Expected=4.600000\n",
      "Month=656, Predicted=6.209794, Expected=5.900000\n",
      "Month=657, Predicted=7.354664, Expected=4.400000\n",
      "Month=658, Predicted=6.738079, Expected=4.500000\n",
      "Month=659, Predicted=6.478889, Expected=7.700000\n",
      "Month=660, Predicted=8.429398, Expected=7.200000\n",
      "Month=661, Predicted=9.017138, Expected=13.700000\n",
      "Month=662, Predicted=13.188929, Expected=7.400000\n",
      "Month=663, Predicted=10.658238, Expected=5.200000\n",
      "Month=664, Predicted=8.194613, Expected=11.100000\n",
      "Month=665, Predicted=10.884578, Expected=29.200000\n",
      "Month=666, Predicted=22.974705, Expected=16.000000\n",
      "Month=667, Predicted=18.810990, Expected=22.200000\n",
      "Month=668, Predicted=21.875600, Expected=16.900000\n",
      "Month=669, Predicted=19.846804, Expected=42.400000\n",
      "Month=670, Predicted=31.754912, Expected=40.600000\n",
      "Month=671, Predicted=38.904422, Expected=31.400000\n",
      "Month=672, Predicted=35.369705, Expected=37.200000\n",
      "Month=673, Predicted=37.435272, Expected=39.000000\n",
      "Month=674, Predicted=39.821144, Expected=34.900000\n",
      "Month=675, Predicted=37.937735, Expected=57.500000\n",
      "Month=676, Predicted=48.712209, Expected=38.300000\n",
      "Month=677, Predicted=40.734538, Expected=41.400000\n",
      "Month=678, Predicted=41.865135, Expected=44.500000\n",
      "Month=679, Predicted=44.878935, Expected=56.700000\n",
      "Month=680, Predicted=53.600559, Expected=55.300000\n",
      "Month=681, Predicted=56.776701, Expected=80.100000\n",
      "Month=682, Predicted=70.529610, Expected=91.200000\n",
      "Month=683, Predicted=88.486930, Expected=51.900000\n",
      "Month=684, Predicted=59.304255, Expected=66.900000\n",
      "Month=685, Predicted=62.705198, Expected=83.700000\n",
      "Month=686, Predicted=77.516660, Expected=87.600000\n",
      "Month=687, Predicted=87.648105, Expected=90.300000\n",
      "Month=688, Predicted=91.727454, Expected=85.700000\n",
      "Month=689, Predicted=89.212829, Expected=91.000000\n",
      "Month=690, Predicted=91.279300, Expected=87.100000\n",
      "Month=691, Predicted=89.777158, Expected=95.200000\n",
      "Month=692, Predicted=94.089933, Expected=106.800000\n",
      "Month=693, Predicted=103.761920, Expected=105.800000\n",
      "Month=694, Predicted=107.332646, Expected=114.600000\n",
      "Month=695, Predicted=113.430697, Expected=97.200000\n",
      "Month=696, Predicted=102.496797, Expected=81.000000\n",
      "Month=697, Predicted=87.811172, Expected=81.500000\n",
      "Month=698, Predicted=84.506612, Expected=88.000000\n",
      "Month=699, Predicted=87.344085, Expected=98.900000\n",
      "Month=700, Predicted=96.031178, Expected=71.400000\n",
      "Month=701, Predicted=77.444718, Expected=107.100000\n",
      "Month=702, Predicted=88.103623, Expected=108.600000\n",
      "Month=703, Predicted=99.243505, Expected=116.700000\n",
      "Month=704, Predicted=115.107703, Expected=100.300000\n",
      "Month=705, Predicted=105.897341, Expected=92.200000\n",
      "Month=706, Predicted=97.510365, Expected=90.100000\n",
      "Month=707, Predicted=93.459291, Expected=97.900000\n",
      "Month=708, Predicted=96.782619, Expected=95.600000\n",
      "Month=709, Predicted=97.399155, Expected=62.300000\n",
      "Month=710, Predicted=69.740500, Expected=77.800000\n",
      "Month=711, Predicted=73.503765, Expected=101.000000\n",
      "Month=712, Predicted=92.014965, Expected=98.500000\n",
      "Month=713, Predicted=99.026031, Expected=56.800000\n",
      "Month=714, Predicted=64.664267, Expected=87.800000\n",
      "Month=715, Predicted=73.097966, Expected=78.000000\n",
      "Month=716, Predicted=73.596112, Expected=82.500000\n",
      "Month=717, Predicted=81.322253, Expected=79.900000\n",
      "Month=718, Predicted=82.370365, Expected=67.200000\n",
      "Month=719, Predicted=72.887926, Expected=53.700000\n",
      "Month=720, Predicted=60.189388, Expected=80.500000\n",
      "Month=721, Predicted=69.344516, Expected=63.100000\n",
      "Month=722, Predicted=63.528514, Expected=64.500000\n",
      "Month=723, Predicted=65.102504, Expected=43.600000\n",
      "Month=724, Predicted=49.731974, Expected=53.700000\n",
      "Month=725, Predicted=52.095380, Expected=64.400000\n",
      "Month=726, Predicted=61.172657, Expected=84.000000\n",
      "Month=727, Predicted=78.276551, Expected=73.400000\n",
      "Month=728, Predicted=76.501693, Expected=62.500000\n",
      "Month=729, Predicted=67.941178, Expected=66.600000\n",
      "Month=730, Predicted=67.758268, Expected=42.000000\n",
      "Month=731, Predicted=48.546346, Expected=50.600000\n",
      "Month=732, Predicted=49.700887, Expected=40.900000\n",
      "Month=733, Predicted=44.467974, Expected=48.300000\n",
      "Month=734, Predicted=47.506701, Expected=56.700000\n",
      "Month=735, Predicted=54.846390, Expected=66.400000\n",
      "Month=736, Predicted=64.539952, Expected=40.600000\n",
      "Month=737, Predicted=46.792704, Expected=53.800000\n",
      "Month=738, Predicted=50.455780, Expected=40.800000\n",
      "Month=739, Predicted=44.166782, Expected=32.700000\n",
      "Month=740, Predicted=37.277841, Expected=48.100000\n",
      "Month=741, Predicted=43.478407, Expected=22.000000\n",
      "Month=742, Predicted=27.110252, Expected=39.900000\n",
      "Month=743, Predicted=33.173648, Expected=37.700000\n",
      "Month=744, Predicted=37.258277, Expected=41.200000\n",
      "Month=745, Predicted=41.734240, Expected=57.700000\n",
      "Month=746, Predicted=52.779537, Expected=47.100000\n",
      "Month=747, Predicted=50.023017, Expected=66.300000\n",
      "Month=748, Predicted=59.615021, Expected=35.800000\n",
      "Month=749, Predicted=41.038099, Expected=40.600000\n",
      "Month=750, Predicted=40.596500, Expected=57.800000\n",
      "Month=751, Predicted=51.428354, Expected=54.700000\n",
      "Month=752, Predicted=55.498799, Expected=54.800000\n",
      "Month=753, Predicted=56.817376, Expected=28.500000\n",
      "Month=754, Predicted=35.491189, Expected=33.900000\n",
      "Month=755, Predicted=34.733678, Expected=57.600000\n",
      "Month=756, Predicted=47.541393, Expected=28.600000\n",
      "Month=757, Predicted=32.541451, Expected=48.700000\n",
      "Month=758, Predicted=40.264708, Expected=39.300000\n",
      "Month=759, Predicted=39.501713, Expected=39.500000\n",
      "Month=760, Predicted=40.914569, Expected=29.400000\n",
      "Month=761, Predicted=34.152874, Expected=34.500000\n",
      "Month=762, Predicted=35.055971, Expected=33.600000\n",
      "Month=763, Predicted=35.308462, Expected=26.800000\n",
      "Month=764, Predicted=30.752440, Expected=37.800000\n",
      "Month=765, Predicted=35.479041, Expected=21.600000\n",
      "Month=766, Predicted=26.123707, Expected=17.100000\n",
      "Month=767, Predicted=20.926528, Expected=24.600000\n",
      "Month=768, Predicted=23.730573, Expected=12.800000\n",
      "Month=769, Predicted=17.064555, Expected=31.600000\n",
      "Month=770, Predicted=25.033253, Expected=38.400000\n",
      "Month=771, Predicted=36.237819, Expected=24.600000\n",
      "Month=772, Predicted=29.447467, Expected=17.600000\n",
      "Month=773, Predicted=22.430049, Expected=12.900000\n",
      "Month=774, Predicted=16.951527, Expected=16.500000\n",
      "Month=775, Predicted=17.370013, Expected=9.300000\n",
      "Month=776, Predicted=12.977975, Expected=12.700000\n",
      "Month=777, Predicted=13.672419, Expected=7.300000\n",
      "Month=778, Predicted=10.554112, Expected=14.100000\n",
      "Month=779, Predicted=13.597883, Expected=9.000000\n",
      "Month=780, Predicted=11.810151, Expected=1.500000\n",
      "Month=781, Predicted=5.933871, Expected=0.000000\n",
      "Month=782, Predicted=2.954654, Expected=0.700000\n",
      "Month=783, Predicted=2.434452, Expected=9.200000\n",
      "Month=784, Predicted=7.619146, Expected=5.100000\n",
      "Month=785, Predicted=7.460709, Expected=2.900000\n",
      "Month=786, Predicted=5.751868, Expected=1.500000\n",
      "Month=787, Predicted=4.077436, Expected=5.000000\n",
      "Month=788, Predicted=5.686557, Expected=4.900000\n",
      "Month=789, Predicted=6.521838, Expected=9.800000\n",
      "Month=790, Predicted=9.898887, Expected=13.500000\n",
      "Month=791, Predicted=13.810487, Expected=9.300000\n",
      "Month=792, Predicted=12.308162, Expected=25.200000\n",
      "Month=793, Predicted=20.364988, Expected=15.600000\n",
      "Month=794, Predicted=18.035243, Expected=15.800000\n",
      "Month=795, Predicted=17.780967, Expected=26.500000\n",
      "Month=796, Predicted=24.045539, Expected=36.600000\n",
      "Month=797, Predicted=34.224840, Expected=26.700000\n",
      "Month=798, Predicted=30.607417, Expected=31.100000\n",
      "Month=799, Predicted=31.897951, Expected=28.600000\n",
      "Month=800, Predicted=30.971453, Expected=34.400000\n",
      "Month=801, Predicted=34.211587, Expected=43.800000\n",
      "Month=802, Predicted=41.761577, Expected=61.700000\n",
      "Month=803, Predicted=56.380591, Expected=59.100000\n",
      "Month=804, Predicted=60.721856, Expected=67.600000\n",
      "Month=805, Predicted=66.703621, Expected=60.900000\n",
      "Month=806, Predicted=64.263920, Expected=59.300000\n",
      "Month=807, Predicted=62.151252, Expected=52.700000\n",
      "Month=808, Predicted=56.818500, Expected=41.000000\n",
      "Month=809, Predicted=46.702263, Expected=104.000000\n",
      "Month=810, Predicted=60.048579, Expected=108.400000\n",
      "Month=811, Predicted=65.672824, Expected=59.200000\n",
      "Month=812, Predicted=50.836807, Expected=79.600000\n",
      "Month=813, Predicted=69.889597, Expected=80.600000\n",
      "Month=814, Predicted=80.573708, Expected=59.400000\n",
      "Month=815, Predicted=65.767313, Expected=77.400000\n",
      "Month=816, Predicted=71.776060, Expected=104.300000\n",
      "Month=817, Predicted=94.460848, Expected=77.300000\n",
      "Month=818, Predicted=81.627340, Expected=114.900000\n",
      "Month=819, Predicted=94.377355, Expected=159.400000\n",
      "Month=820, Predicted=155.011997, Expected=160.000000\n",
      "Month=821, Predicted=164.017307, Expected=176.000000\n",
      "Month=822, Predicted=172.262115, Expected=135.600000\n",
      "Month=823, Predicted=142.798211, Expected=132.400000\n",
      "Month=824, Predicted=135.969940, Expected=153.800000\n",
      "Month=825, Predicted=144.959745, Expected=136.000000\n",
      "Month=826, Predicted=137.927641, Expected=146.400000\n",
      "Month=827, Predicted=143.596345, Expected=147.500000\n",
      "Month=828, Predicted=147.984434, Expected=130.000000\n",
      "Month=829, Predicted=135.908004, Expected=88.300000\n",
      "Month=830, Predicted=96.220654, Expected=125.300000\n",
      "Month=831, Predicted=106.894203, Expected=143.200000\n",
      "Month=832, Predicted=134.597006, Expected=162.400000\n",
      "Month=833, Predicted=161.389992, Expected=145.500000\n",
      "Month=834, Predicted=151.646279, Expected=91.700000\n",
      "Month=835, Predicted=99.620654, Expected=103.000000\n",
      "Month=836, Predicted=101.961034, Expected=110.000000\n",
      "Month=837, Predicted=108.356688, Expected=80.300000\n",
      "Month=838, Predicted=86.846700, Expected=89.000000\n",
      "Month=839, Predicted=87.860562, Expected=105.400000\n",
      "Month=840, Predicted=99.409468, Expected=90.300000\n",
      "Month=841, Predicted=93.534997, Expected=79.500000\n",
      "Month=842, Predicted=84.764733, Expected=120.100000\n",
      "Month=843, Predicted=97.720643, Expected=88.400000\n",
      "Month=844, Predicted=86.538746, Expected=102.100000\n",
      "Month=845, Predicted=96.287547, Expected=107.600000\n",
      "Month=846, Predicted=106.591772, Expected=109.900000\n",
      "Month=847, Predicted=111.228146, Expected=105.500000\n",
      "Month=848, Predicted=108.978730, Expected=92.900000\n",
      "Month=849, Predicted=98.727580, Expected=114.600000\n",
      "Month=850, Predicted=106.618572, Expected=103.500000\n",
      "Month=851, Predicted=104.263759, Expected=112.000000\n",
      "Month=852, Predicted=110.253098, Expected=83.900000\n",
      "Month=853, Predicted=90.225782, Expected=86.700000\n",
      "Month=854, Predicted=88.149377, Expected=107.000000\n",
      "Month=855, Predicted=98.906628, Expected=98.300000\n",
      "Month=856, Predicted=99.092900, Expected=76.200000\n",
      "Month=857, Predicted=82.545979, Expected=47.900000\n",
      "Month=858, Predicted=55.592448, Expected=44.800000\n",
      "Month=859, Predicted=49.280580, Expected=66.900000\n",
      "Month=860, Predicted=58.149620, Expected=68.200000\n",
      "Month=861, Predicted=66.492150, Expected=47.500000\n",
      "Month=862, Predicted=53.214363, Expected=47.400000\n",
      "Month=863, Predicted=50.095813, Expected=55.400000\n",
      "Month=864, Predicted=54.004479, Expected=49.200000\n",
      "Month=865, Predicted=52.038465, Expected=60.800000\n",
      "Month=866, Predicted=58.117475, Expected=64.200000\n",
      "Month=867, Predicted=64.039753, Expected=46.400000\n",
      "Month=868, Predicted=52.170717, Expected=32.000000\n",
      "Month=869, Predicted=38.630364, Expected=44.600000\n",
      "Month=870, Predicted=42.197253, Expected=38.200000\n",
      "Month=871, Predicted=40.507824, Expected=67.800000\n",
      "Month=872, Predicted=54.393043, Expected=61.300000\n",
      "Month=873, Predicted=58.450949, Expected=28.000000\n",
      "Month=874, Predicted=34.656217, Expected=34.300000\n",
      "Month=875, Predicted=34.151450, Expected=28.900000\n",
      "Month=876, Predicted=31.498849, Expected=29.300000\n",
      "Month=877, Predicted=31.137853, Expected=14.600000\n",
      "Month=878, Predicted=20.350345, Expected=22.200000\n",
      "Month=879, Predicted=21.882730, Expected=33.800000\n",
      "Month=880, Predicted=30.395018, Expected=29.100000\n",
      "Month=881, Predicted=31.277085, Expected=11.500000\n",
      "Month=882, Predicted=17.878541, Expected=23.900000\n",
      "Month=883, Predicted=21.474640, Expected=12.500000\n",
      "Month=884, Predicted=15.979717, Expected=14.600000\n",
      "Month=885, Predicted=15.977624, Expected=2.400000\n",
      "Month=886, Predicted=7.471625, Expected=12.700000\n",
      "Month=887, Predicted=10.902897, Expected=17.700000\n",
      "Month=888, Predicted=16.837063, Expected=9.900000\n",
      "Month=889, Predicted=13.610541, Expected=14.300000\n",
      "Month=890, Predicted=15.018906, Expected=15.000000\n",
      "Month=891, Predicted=16.312297, Expected=31.200000\n",
      "Month=892, Predicted=26.103270, Expected=2.300000\n",
      "Month=893, Predicted=7.860551, Expected=5.100000\n",
      "Month=894, Predicted=6.196463, Expected=1.600000\n",
      "Month=895, Predicted=4.076545, Expected=15.200000\n",
      "Month=896, Predicted=11.304565, Expected=8.800000\n",
      "Month=897, Predicted=10.947766, Expected=9.900000\n",
      "Month=898, Predicted=11.601696, Expected=14.300000\n",
      "Month=899, Predicted=14.563998, Expected=9.900000\n",
      "Month=900, Predicted=12.835829, Expected=8.200000\n",
      "Month=901, Predicted=10.950341, Expected=24.400000\n",
      "Month=902, Predicted=19.188047, Expected=8.700000\n",
      "Month=903, Predicted=12.065286, Expected=11.700000\n",
      "Month=904, Predicted=12.600671, Expected=15.800000\n",
      "Month=905, Predicted=15.859032, Expected=21.200000\n",
      "Month=906, Predicted=20.877205, Expected=13.400000\n",
      "Month=907, Predicted=17.207275, Expected=5.900000\n",
      "Month=908, Predicted=10.594639, Expected=6.300000\n",
      "Month=909, Predicted=8.635947, Expected=16.400000\n",
      "Month=910, Predicted=14.069865, Expected=6.700000\n",
      "Month=911, Predicted=10.118192, Expected=14.500000\n",
      "Month=912, Predicted=13.628413, Expected=2.300000\n",
      "Month=913, Predicted=6.710396, Expected=3.300000\n",
      "Month=914, Predicted=5.354099, Expected=6.000000\n",
      "Month=915, Predicted=6.783878, Expected=7.800000\n",
      "Month=916, Predicted=8.799943, Expected=0.100000\n",
      "Month=917, Predicted=4.143882, Expected=5.800000\n",
      "Month=918, Predicted=5.957634, Expected=6.400000\n",
      "Month=919, Predicted=7.576425, Expected=0.100000\n",
      "Month=920, Predicted=3.825342, Expected=0.000000\n",
      "Month=921, Predicted=2.347776, Expected=5.300000\n",
      "Month=922, Predicted=5.173385, Expected=1.100000\n",
      "Month=923, Predicted=3.806341, Expected=4.100000\n",
      "Month=924, Predicted=5.128775, Expected=0.500000\n",
      "Month=925, Predicted=3.325390, Expected=0.800000\n",
      "Month=926, Predicted=2.804083, Expected=0.600000\n",
      "Month=927, Predicted=2.534704, Expected=0.000000\n",
      "Month=928, Predicted=2.086597, Expected=6.200000\n",
      "Month=929, Predicted=5.763598, Expected=2.400000\n",
      "Month=930, Predicted=4.959713, Expected=4.800000\n",
      "Month=931, Predicted=6.057613, Expected=7.500000\n",
      "Month=932, Predicted=8.290805, Expected=10.700000\n",
      "Month=933, Predicted=11.301300, Expected=6.100000\n",
      "Month=934, Predicted=9.238702, Expected=12.300000\n",
      "Month=935, Predicted=12.118572, Expected=12.900000\n",
      "Month=936, Predicted=14.095344, Expected=7.200000\n",
      "Month=937, Predicted=10.800846, Expected=24.000000\n",
      "Month=938, Predicted=18.639003, Expected=27.500000\n",
      "Month=939, Predicted=26.638204, Expected=19.500000\n",
      "Month=940, Predicted=23.465269, Expected=19.300000\n",
      "Month=941, Predicted=21.856163, Expected=23.500000\n",
      "Month=942, Predicted=23.878643, Expected=34.100000\n",
      "Month=943, Predicted=31.518912, Expected=21.900000\n",
      "Month=944, Predicted=25.941152, Expected=48.100000\n",
      "Month=945, Predicted=36.922227, Expected=66.000000\n",
      "Month=946, Predicted=60.929843, Expected=43.000000\n",
      "Month=947, Predicted=48.492985, Expected=30.700000\n",
      "Month=948, Predicted=36.843018, Expected=29.600000\n",
      "Month=949, Predicted=32.884646, Expected=36.400000\n",
      "Month=950, Predicted=35.682007, Expected=53.200000\n",
      "Month=951, Predicted=47.570381, Expected=51.500000\n",
      "Month=952, Predicted=52.483095, Expected=51.700000\n",
      "Month=953, Predicted=53.786266, Expected=43.500000\n",
      "Month=954, Predicted=48.012921, Expected=60.500000\n",
      "Month=955, Predicted=55.107402, Expected=76.900000\n",
      "Month=956, Predicted=71.784506, Expected=58.000000\n",
      "Month=957, Predicted=62.600464, Expected=53.200000\n",
      "Month=958, Predicted=57.213264, Expected=64.000000\n",
      "Month=959, Predicted=61.636217, Expected=54.800000\n",
      "Month=960, Predicted=57.958812, Expected=47.300000\n",
      "Month=961, Predicted=51.781728, Expected=45.000000\n",
      "Month=962, Predicted=48.217576, Expected=69.300000\n",
      "Month=963, Predicted=59.099525, Expected=67.500000\n",
      "Month=964, Predicted=65.893018, Expected=95.800000\n",
      "Month=965, Predicted=85.353443, Expected=64.100000\n",
      "Month=966, Predicted=68.755121, Expected=45.200000\n",
      "Month=967, Predicted=51.959851, Expected=45.400000\n",
      "Month=968, Predicted=48.363170, Expected=40.400000\n",
      "Month=969, Predicted=43.927069, Expected=57.700000\n",
      "Month=970, Predicted=51.830711, Expected=59.200000\n",
      "Month=971, Predicted=58.666396, Expected=84.400000\n",
      "Month=972, Predicted=75.330174, Expected=41.800000\n",
      "Month=973, Predicted=48.324201, Expected=60.600000\n",
      "Month=974, Predicted=53.049715, Expected=46.900000\n",
      "Month=975, Predicted=48.083695, Expected=42.800000\n",
      "Month=976, Predicted=45.527712, Expected=82.100000\n",
      "Month=977, Predicted=61.059165, Expected=32.100000\n",
      "Month=978, Predicted=36.195081, Expected=76.500000\n",
      "Month=979, Predicted=46.978335, Expected=80.600000\n",
      "Month=980, Predicted=58.081812, Expected=46.000000\n",
      "Month=981, Predicted=45.846047, Expected=52.600000\n",
      "Month=982, Predicted=50.420015, Expected=83.800000\n",
      "Month=983, Predicted=70.810565, Expected=84.500000\n",
      "Month=984, Predicted=82.748788, Expected=75.900000\n",
      "Month=985, Predicted=80.058393, Expected=91.500000\n",
      "Month=986, Predicted=87.148675, Expected=86.900000\n",
      "Month=987, Predicted=88.360011, Expected=86.800000\n",
      "Month=988, Predicted=88.820301, Expected=76.100000\n",
      "Month=989, Predicted=81.134597, Expected=66.500000\n",
      "Month=990, Predicted=71.972900, Expected=51.200000\n",
      "Month=991, Predicted=57.923768, Expected=53.100000\n",
      "Month=992, Predicted=55.555922, Expected=55.800000\n",
      "Month=993, Predicted=56.576092, Expected=61.900000\n",
      "Month=994, Predicted=61.216684, Expected=47.800000\n",
      "Month=995, Predicted=52.793308, Expected=36.600000\n",
      "Month=996, Predicted=42.426563, Expected=47.200000\n",
      "Month=997, Predicted=45.466088, Expected=42.800000\n",
      "Month=998, Predicted=44.841681, Expected=71.800000\n",
      "Month=999, Predicted=58.918149, Expected=49.800000\n",
      "Month=1000, Predicted=51.040407, Expected=55.000000\n",
      "Month=1001, Predicted=54.263536, Expected=73.000000\n",
      "Month=1002, Predicted=66.933715, Expected=83.700000\n",
      "Month=1003, Predicted=81.654067, Expected=66.500000\n",
      "Month=1004, Predicted=71.944384, Expected=50.000000\n",
      "Month=1005, Predicted=56.954641, Expected=39.600000\n",
      "Month=1006, Predicted=45.811846, Expected=38.700000\n",
      "Month=1007, Predicted=41.963336, Expected=33.300000\n",
      "Month=1008, Predicted=37.065925, Expected=21.700000\n",
      "Month=1009, Predicted=27.264023, Expected=29.900000\n",
      "Month=1010, Predicted=29.226001, Expected=25.900000\n",
      "Month=1011, Predicted=28.164058, Expected=57.300000\n",
      "Month=1012, Predicted=42.638698, Expected=43.700000\n",
      "Month=1013, Predicted=41.769231, Expected=30.700000\n",
      "Month=1014, Predicted=34.858370, Expected=27.100000\n",
      "Month=1015, Predicted=30.639180, Expected=30.300000\n",
      "Month=1016, Predicted=31.228301, Expected=16.900000\n",
      "Month=1017, Predicted=22.089472, Expected=21.400000\n",
      "Month=1018, Predicted=22.257067, Expected=8.600000\n",
      "Month=1019, Predicted=13.578746, Expected=0.300000\n",
      "Month=1020, Predicted=5.393376, Expected=12.400000\n",
      "Month=1021, Predicted=9.645949, Expected=10.300000\n",
      "Month=1022, Predicted=11.438962, Expected=13.200000\n",
      "Month=1023, Predicted=14.084148, Expected=4.200000\n",
      "Month=1024, Predicted=8.559493, Expected=6.900000\n",
      "Month=1025, Predicted=8.352655, Expected=20.000000\n",
      "Month=1026, Predicted=16.171621, Expected=15.700000\n",
      "Month=1027, Predicted=17.487111, Expected=23.300000\n",
      "Month=1028, Predicted=22.514087, Expected=21.400000\n",
      "Month=1029, Predicted=23.416962, Expected=7.400000\n",
      "Month=1030, Predicted=13.184391, Expected=6.600000\n",
      "Month=1031, Predicted=9.712812, Expected=6.900000\n",
      "Month=1032, Predicted=8.769388, Expected=20.700000\n",
      "Month=1033, Predicted=16.591846, Expected=12.700000\n",
      "Month=1034, Predicted=15.175195, Expected=7.100000\n",
      "Month=1035, Predicted=10.976192, Expected=7.800000\n",
      "Month=1036, Predicted=9.863879, Expected=5.100000\n",
      "Month=1037, Predicted=7.810756, Expected=7.000000\n",
      "Month=1038, Predicted=8.334188, Expected=7.100000\n",
      "Month=1039, Predicted=8.781441, Expected=3.100000\n",
      "Month=1040, Predicted=6.247094, Expected=2.800000\n",
      "Month=1041, Predicted=5.067483, Expected=8.800000\n",
      "Month=1042, Predicted=8.400923, Expected=2.100000\n",
      "Month=1043, Predicted=5.425276, Expected=10.700000\n",
      "Month=1044, Predicted=9.474108, Expected=6.700000\n",
      "Month=1045, Predicted=9.017555, Expected=0.800000\n",
      "Month=1046, Predicted=4.714213, Expected=8.500000\n",
      "Month=1047, Predicted=7.725020, Expected=7.000000\n",
      "Month=1048, Predicted=8.639737, Expected=4.300000\n",
      "Month=1049, Predicted=7.116990, Expected=2.400000\n",
      "Month=1050, Predicted=5.158518, Expected=6.400000\n",
      "Month=1051, Predicted=6.932796, Expected=9.700000\n",
      "Month=1052, Predicted=10.089462, Expected=20.600000\n",
      "Month=1053, Predicted=18.103364, Expected=6.500000\n",
      "Month=1054, Predicted=10.940223, Expected=2.100000\n",
      "Month=1055, Predicted=6.001632, Expected=0.200000\n",
      "Month=1056, Predicted=3.089533, Expected=6.700000\n",
      "Month=1057, Predicted=6.123283, Expected=5.300000\n",
      "Month=1058, Predicted=7.014929, Expected=0.600000\n",
      "Month=1059, Predicted=4.035846, Expected=5.100000\n",
      "Month=1060, Predicted=5.631767, Expected=1.600000\n",
      "Month=1061, Predicted=4.214754, Expected=4.800000\n",
      "Month=1062, Predicted=5.698511, Expected=1.300000\n",
      "Month=1063, Predicted=4.062632, Expected=11.600000\n",
      "Month=1064, Predicted=9.482378, Expected=8.500000\n",
      "Month=1065, Predicted=10.378767, Expected=17.200000\n",
      "Month=1066, Predicted=15.880456, Expected=11.200000\n",
      "Month=1067, Predicted=14.181771, Expected=9.600000\n",
      "Month=1068, Predicted=12.367571, Expected=7.800000\n",
      "Month=1069, Predicted=10.456460, Expected=13.500000\n",
      "Month=1070, Predicted=13.306415, Expected=22.200000\n",
      "Month=1071, Predicted=20.391214, Expected=10.400000\n",
      "Month=1072, Predicted=14.661936, Expected=20.500000\n",
      "Month=1073, Predicted=18.732200, Expected=41.100000\n",
      "Month=1074, Predicted=33.649465, Expected=48.300000\n",
      "Month=1075, Predicted=47.229006, Expected=58.800000\n",
      "Month=1076, Predicted=57.592895, Expected=33.200000\n",
      "Month=1077, Predicted=39.566287, Expected=53.800000\n",
      "Month=1078, Predicted=46.235837, Expected=51.500000\n",
      "Month=1079, Predicted=50.664232, Expected=41.900000\n",
      "Month=1080, Predicted=46.038791, Expected=32.300000\n",
      "Month=1081, Predicted=37.607339, Expected=69.100000\n",
      "Month=1082, Predicted=49.946237, Expected=75.600000\n",
      "Month=1083, Predicted=66.740155, Expected=49.900000\n",
      "Month=1084, Predicted=54.277868, Expected=69.600000\n",
      "Month=1085, Predicted=62.065931, Expected=79.600000\n",
      "Month=1086, Predicted=76.258197, Expected=76.300000\n",
      "Month=1087, Predicted=78.849187, Expected=76.800000\n",
      "Month=1088, Predicted=79.041917, Expected=101.400000\n",
      "Month=1089, Predicted=91.397287, Expected=62.800000\n",
      "Month=1090, Predicted=68.357433, Expected=70.500000\n",
      "Month=1091, Predicted=68.850956, Expected=65.400000\n",
      "Month=1092, Predicted=67.386189, Expected=78.600000\n",
      "Month=1093, Predicted=74.929027, Expected=75.000000\n",
      "Month=1094, Predicted=76.638664, Expected=73.000000\n",
      "Month=1095, Predicted=75.717165, Expected=65.700000\n",
      "Month=1096, Predicted=70.063326, Expected=88.100000\n",
      "Month=1097, Predicted=79.365732, Expected=84.700000\n",
      "Month=1098, Predicted=83.919701, Expected=88.200000\n",
      "Month=1099, Predicted=88.745114, Expected=88.800000\n",
      "Month=1100, Predicted=90.516069, Expected=129.200000\n",
      "Month=1101, Predicted=108.108553, Expected=77.900000\n",
      "Month=1102, Predicted=82.378251, Expected=79.700000\n",
      "Month=1103, Predicted=79.801159, Expected=75.100000\n",
      "Month=1104, Predicted=77.412158, Expected=93.800000\n",
      "Month=1105, Predicted=87.097060, Expected=83.200000\n",
      "Month=1106, Predicted=84.987198, Expected=84.600000\n",
      "Month=1107, Predicted=85.985315, Expected=52.300000\n",
      "Month=1108, Predicted=59.595839, Expected=81.600000\n",
      "Month=1109, Predicted=68.052465, Expected=101.200000\n",
      "Month=1110, Predicted=94.205816, Expected=98.900000\n",
      "Month=1111, Predicted=101.156448, Expected=106.000000\n",
      "Month=1112, Predicted=106.047081, Expected=70.300000\n",
      "Month=1113, Predicted=77.679881, Expected=65.900000\n",
      "Month=1114, Predicted=70.204607, Expected=75.500000\n",
      "Month=1115, Predicted=73.553185, Expected=56.600000\n",
      "Month=1116, Predicted=61.566778, Expected=60.000000\n",
      "Month=1117, Predicted=61.009315, Expected=63.300000\n",
      "Month=1118, Predicted=63.527851, Expected=67.200000\n",
      "Month=1119, Predicted=67.403234, Expected=61.000000\n",
      "Month=1120, Predicted=64.508485, Expected=76.900000\n",
      "Month=1121, Predicted=72.078462, Expected=67.500000\n",
      "Month=1122, Predicted=69.838487, Expected=71.500000\n",
      "Month=1123, Predicted=72.046638, Expected=47.800000\n",
      "Month=1124, Predicted=54.192679, Expected=68.900000\n",
      "Month=1125, Predicted=61.004451, Expected=57.700000\n",
      "Month=1126, Predicted=58.378370, Expected=67.900000\n",
      "Month=1127, Predicted=65.341740, Expected=47.200000\n",
      "Month=1128, Predicted=52.429058, Expected=70.700000\n",
      "Month=1129, Predicted=60.972734, Expected=29.000000\n",
      "Month=1130, Predicted=34.963292, Expected=57.400000\n",
      "Month=1131, Predicted=42.454505, Expected=52.000000\n",
      "Month=1132, Predicted=46.231087, Expected=43.800000\n",
      "Month=1133, Predicted=45.545764, Expected=27.700000\n",
      "Month=1134, Predicted=33.755331, Expected=49.000000\n",
      "Month=1135, Predicted=41.337173, Expected=45.000000\n",
      "Month=1136, Predicted=44.612108, Expected=27.200000\n",
      "Month=1137, Predicted=32.828883, Expected=61.300000\n",
      "Month=1138, Predicted=44.239963, Expected=28.400000\n",
      "Month=1139, Predicted=29.747199, Expected=38.000000\n",
      "Month=1140, Predicted=34.433010, Expected=42.600000\n",
      "Month=1141, Predicted=41.636864, Expected=40.600000\n",
      "Month=1142, Predicted=42.909903, Expected=29.400000\n",
      "Month=1143, Predicted=34.724384, Expected=29.100000\n",
      "Month=1144, Predicted=31.916240, Expected=31.000000\n",
      "Month=1145, Predicted=32.225580, Expected=20.000000\n",
      "Month=1146, Predicted=24.776157, Expected=11.300000\n",
      "Month=1147, Predicted=16.467712, Expected=27.600000\n",
      "Month=1148, Predicted=22.606790, Expected=21.800000\n",
      "Month=1149, Predicted=23.072068, Expected=48.100000\n",
      "Month=1150, Predicted=37.261380, Expected=14.300000\n",
      "Month=1151, Predicted=18.873239, Expected=8.400000\n",
      "Month=1152, Predicted=12.122735, Expected=33.300000\n",
      "Month=1153, Predicted=22.391724, Expected=30.200000\n",
      "Month=1154, Predicted=28.177886, Expected=36.400000\n",
      "Month=1155, Predicted=35.921173, Expected=38.300000\n",
      "Month=1156, Predicted=39.580557, Expected=14.500000\n",
      "Month=1157, Predicted=21.178774, Expected=25.800000\n",
      "Month=1158, Predicted=23.793976, Expected=22.300000\n",
      "Month=1159, Predicted=23.896614, Expected=9.000000\n",
      "Month=1160, Predicted=14.476545, Expected=31.400000\n",
      "Month=1161, Predicted=22.871821, Expected=34.800000\n",
      "Month=1162, Predicted=32.652658, Expected=34.400000\n",
      "Month=1163, Predicted=36.245520, Expected=30.900000\n",
      "Month=1164, Predicted=34.238467, Expected=12.600000\n",
      "Month=1165, Predicted=19.273488, Expected=19.500000\n",
      "Month=1166, Predicted=19.834994, Expected=9.200000\n",
      "Month=1167, Predicted=13.395429, Expected=18.100000\n",
      "Month=1168, Predicted=16.749123, Expected=14.200000\n",
      "Month=1169, Predicted=16.344896, Expected=7.700000\n",
      "Month=1170, Predicted=11.722573, Expected=20.500000\n",
      "Month=1171, Predicted=17.284651, Expected=13.500000\n",
      "Month=1172, Predicted=15.875258, Expected=2.900000\n",
      "Month=1173, Predicted=8.006271, Expected=8.400000\n",
      "Month=1174, Predicted=8.857701, Expected=13.000000\n",
      "Month=1175, Predicted=12.693938, Expected=7.800000\n",
      "Month=1176, Predicted=10.847857, Expected=10.500000\n",
      "Month=1177, Predicted=11.732956, Expected=9.400000\n",
      "Month=1178, Predicted=11.470859, Expected=13.600000\n",
      "Month=1179, Predicted=14.003921, Expected=8.600000\n",
      "Month=1180, Predicted=11.712658, Expected=16.000000\n",
      "Month=1181, Predicted=15.275110, Expected=15.200000\n",
      "Month=1182, Predicted=16.724012, Expected=12.100000\n",
      "Month=1183, Predicted=15.038196, Expected=8.300000\n",
      "Month=1184, Predicted=11.697481, Expected=4.300000\n",
      "Month=1185, Predicted=7.798179, Expected=8.300000\n",
      "Month=1186, Predicted=8.938179, Expected=12.900000\n",
      "Month=1187, Predicted=12.742168, Expected=4.500000\n",
      "Month=1188, Predicted=8.414902, Expected=0.300000\n",
      "Month=1189, Predicted=4.057606, Expected=0.200000\n",
      "Month=1190, Predicted=2.458962, Expected=2.400000\n",
      "Month=1191, Predicted=3.445882, Expected=4.500000\n",
      "Month=1192, Predicted=5.433319, Expected=0.000000\n",
      "Month=1193, Predicted=3.144816, Expected=10.200000\n",
      "Month=1194, Predicted=8.195909, Expected=5.800000\n",
      "Month=1195, Predicted=8.022524, Expected=0.700000\n",
      "Month=1196, Predicted=4.386366, Expected=1.000000\n",
      "Month=1197, Predicted=3.176783, Expected=0.600000\n",
      "Month=1198, Predicted=2.587941, Expected=3.700000\n",
      "Month=1199, Predicted=4.443359, Expected=3.800000\n",
      "Month=1200, Predicted=5.414238, Expected=0.000000\n",
      "Month=1201, Predicted=3.114835, Expected=5.200000\n",
      "Month=1202, Predicted=5.381694, Expected=0.000000\n",
      "Month=1203, Predicted=3.037776, Expected=12.400000\n",
      "Month=1204, Predicted=9.303760, Expected=0.000000\n",
      "Month=1205, Predicted=3.681042, Expected=2.800000\n",
      "Month=1206, Predicted=3.997829, Expected=1.400000\n",
      "Month=1207, Predicted=3.487924, Expected=0.900000\n",
      "Month=1208, Predicted=3.007670, Expected=2.300000\n",
      "Month=1209, Predicted=3.730260, Expected=7.600000\n",
      "Month=1210, Predicted=7.426685, Expected=16.300000\n",
      "Month=1211, Predicted=14.646485, Expected=10.300000\n",
      "Month=1212, Predicted=13.347414, Expected=1.100000\n",
      "Month=1213, Predicted=6.094992, Expected=8.300000\n",
      "Month=1214, Predicted=7.987789, Expected=17.000000\n",
      "Month=1215, Predicted=14.940722, Expected=13.500000\n",
      "Month=1216, Predicted=15.744184, Expected=26.100000\n",
      "Month=1217, Predicted=23.066626, Expected=14.600000\n",
      "Month=1218, Predicted=18.237630, Expected=16.300000\n",
      "Month=1219, Predicted=17.962984, Expected=27.900000\n",
      "Month=1220, Predicted=24.879355, Expected=28.800000\n",
      "Month=1221, Predicted=29.429712, Expected=11.100000\n",
      "Month=1222, Predicted=17.088443, Expected=38.900000\n",
      "Month=1223, Predicted=26.769264, Expected=44.500000\n",
      "Month=1224, Predicted=40.321153, Expected=45.600000\n",
      "Month=1225, Predicted=46.935199, Expected=31.600000\n",
      "Month=1226, Predicted=37.446803, Expected=24.500000\n",
      "Month=1227, Predicted=29.614947, Expected=37.200000\n",
      "Month=1228, Predicted=34.158761, Expected=43.000000\n",
      "Month=1229, Predicted=41.628413, Expected=39.500000\n",
      "Month=1230, Predicted=42.097176, Expected=41.900000\n",
      "Month=1231, Predicted=43.292922, Expected=50.600000\n",
      "Month=1232, Predicted=49.033187, Expected=58.200000\n",
      "Month=1233, Predicted=56.906045, Expected=30.100000\n",
      "Month=1234, Predicted=36.619712, Expected=54.200000\n",
      "Month=1235, Predicted=44.182455, Expected=38.000000\n",
      "Month=1236, Predicted=38.622370, Expected=54.600000\n",
      "Month=1237, Predicted=48.529507, Expected=54.800000\n",
      "Month=1238, Predicted=54.895285, Expected=85.800000\n",
      "Month=1239, Predicted=72.990798, Expected=56.500000\n",
      "Month=1240, Predicted=59.712252, Expected=39.300000\n",
      "Month=1241, Predicted=45.517216, Expected=48.000000\n",
      "Month=1242, Predicted=47.189404, Expected=49.000000\n",
      "Month=1243, Predicted=49.594504, Expected=73.000000\n",
      "Month=1244, Predicted=63.676821, Expected=58.800000\n",
      "Month=1245, Predicted=60.307389, Expected=55.000000\n",
      "Month=1246, Predicted=57.951117, Expected=78.700000\n",
      "Month=1247, Predicted=69.103524, Expected=107.200000\n",
      "Month=1248, Predicted=99.765787, Expected=55.500000\n",
      "Month=1249, Predicted=63.335892, Expected=45.500000\n",
      "Month=1250, Predicted=51.299967, Expected=31.300000\n",
      "Month=1251, Predicted=37.815652, Expected=64.500000\n",
      "Month=1252, Predicted=48.534399, Expected=55.300000\n",
      "Month=1253, Predicted=50.228092, Expected=57.700000\n",
      "Month=1254, Predicted=57.119893, Expected=63.200000\n",
      "Month=1255, Predicted=63.228377, Expected=103.600000\n",
      "Month=1256, Predicted=83.828027, Expected=47.700000\n",
      "Month=1257, Predicted=53.625398, Expected=56.100000\n",
      "Month=1258, Predicted=53.458675, Expected=17.800000\n",
      "Month=1259, Predicted=24.835464, Expected=38.900000\n",
      "Month=1260, Predicted=29.940363, Expected=64.700000\n",
      "Month=1261, Predicted=55.529412, Expected=76.400000\n",
      "Month=1262, Predicted=76.043619, Expected=108.200000\n",
      "Month=1263, Predicted=96.906244, Expected=60.700000\n",
      "Month=1264, Predicted=67.438792, Expected=52.600000\n",
      "Month=1265, Predicted=57.384253, Expected=42.900000\n",
      "Month=1266, Predicted=48.091255, Expected=40.400000\n",
      "Month=1267, Predicted=43.786987, Expected=49.700000\n",
      "Month=1268, Predicted=47.877172, Expected=54.300000\n",
      "Month=1269, Predicted=53.725335, Expected=85.000000\n",
      "Month=1270, Predicted=72.260138, Expected=65.400000\n",
      "Month=1271, Predicted=66.674767, Expected=61.500000\n",
      "Month=1272, Predicted=64.279304, Expected=47.300000\n",
      "Month=1273, Predicted=53.203497, Expected=39.200000\n",
      "Month=1274, Predicted=44.516619, Expected=33.900000\n",
      "Month=1275, Predicted=38.243544, Expected=28.700000\n",
      "Month=1276, Predicted=32.721853, Expected=57.600000\n",
      "Month=1277, Predicted=44.260951, Expected=40.800000\n",
      "Month=1278, Predicted=40.122677, Expected=48.100000\n",
      "Month=1279, Predicted=46.357833, Expected=39.500000\n",
      "Month=1280, Predicted=43.055804, Expected=90.500000\n",
      "Month=1281, Predicted=59.220312, Expected=86.900000\n",
      "Month=1282, Predicted=66.479714, Expected=32.300000\n",
      "Month=1283, Predicted=37.640827, Expected=45.500000\n",
      "Month=1284, Predicted=39.846847, Expected=39.500000\n",
      "Month=1285, Predicted=39.892236, Expected=56.700000\n",
      "Month=1286, Predicted=50.986530, Expected=46.600000\n",
      "Month=1287, Predicted=49.041684, Expected=66.300000\n",
      "Month=1288, Predicted=59.331869, Expected=32.300000\n",
      "Month=1289, Predicted=37.999948, Expected=36.000000\n",
      "Month=1290, Predicted=36.493637, Expected=22.600000\n",
      "Month=1291, Predicted=27.428951, Expected=35.800000\n",
      "Month=1292, Predicted=32.354863, Expected=23.100000\n",
      "Month=1293, Predicted=26.508677, Expected=38.800000\n",
      "Month=1294, Predicted=33.821577, Expected=58.400000\n",
      "Month=1295, Predicted=52.173891, Expected=55.800000\n",
      "Month=1296, Predicted=57.519408, Expected=54.200000\n",
      "Month=1297, Predicted=57.103998, Expected=26.400000\n",
      "Month=1298, Predicted=33.647741, Expected=31.500000\n",
      "Month=1299, Predicted=32.579432, Expected=21.400000\n",
      "Month=1300, Predicted=25.718005, Expected=8.400000\n",
      "Month=1301, Predicted=14.404906, Expected=22.200000\n",
      "Month=1302, Predicted=18.870882, Expected=12.300000\n",
      "Month=1303, Predicted=15.105420, Expected=14.100000\n",
      "Month=1304, Predicted=15.488019, Expected=11.500000\n",
      "Month=1305, Predicted=14.071374, Expected=26.200000\n",
      "Month=1306, Predicted=21.842861, Expected=38.300000\n",
      "Month=1307, Predicted=35.085092, Expected=4.900000\n",
      "Month=1308, Predicted=11.631280, Expected=5.800000\n",
      "Month=1309, Predicted=8.084132, Expected=3.400000\n",
      "Month=1310, Predicted=5.814572, Expected=9.000000\n",
      "Month=1311, Predicted=8.733241, Expected=7.800000\n",
      "Month=1312, Predicted=9.567670, Expected=16.500000\n",
      "Month=1313, Predicted=15.089890, Expected=9.000000\n",
      "Month=1314, Predicted=12.320319, Expected=2.200000\n",
      "Month=1315, Predicted=6.591525, Expected=3.500000\n",
      "Month=1316, Predicted=5.436498, Expected=4.000000\n",
      "Month=1317, Predicted=5.566961, Expected=4.000000\n",
      "Month=1318, Predicted=5.784068, Expected=2.600000\n",
      "Month=1319, Predicted=4.948408, Expected=4.200000\n",
      "Month=1320, Predicted=5.621896, Expected=2.200000\n",
      "Month=1321, Predicted=4.629768, Expected=0.300000\n",
      "Month=1322, Predicted=2.957101, Expected=0.000000\n",
      "Month=1323, Predicted=2.129061, Expected=4.900000\n",
      "Month=1324, Predicted=4.952270, Expected=4.500000\n",
      "Month=1325, Predicted=6.126024, Expected=4.400000\n",
      "Month=1326, Predicted=6.374279, Expected=4.100000\n",
      "Month=1327, Predicted=6.151736, Expected=3.000000\n",
      "Month=1328, Predicted=5.302146, Expected=0.300000\n",
      "Month=1329, Predicted=3.163882, Expected=9.500000\n",
      "Month=1330, Predicted=7.836804, Expected=4.600000\n",
      "Month=1331, Predicted=7.061082, Expected=1.100000\n",
      "Month=1332, Predicted=4.351677, Expected=6.400000\n",
      "Month=1333, Predicted=6.535026, Expected=2.300000\n",
      "Month=1334, Predicted=4.997156, Expected=2.900000\n",
      "Month=1335, Predicted=4.790550, Expected=0.500000\n",
      "Month=1336, Predicted=3.150331, Expected=0.900000\n",
      "Month=1337, Predicted=2.795973, Expected=0.000000\n",
      "Month=1338, Predicted=2.150631, Expected=0.000000\n",
      "Month=1339, Predicted=1.931742, Expected=1.700000\n",
      "Month=1340, Predicted=2.979539, Expected=0.200000\n",
      "Month=1341, Predicted=2.459340, Expected=1.200000\n",
      "Month=1342, Predicted=2.845191, Expected=3.100000\n",
      "Month=1343, Predicted=4.257612, Expected=0.700000\n",
      "Month=1344, Predicted=3.238161, Expected=3.800000\n",
      "Month=1345, Predicted=4.728913, Expected=2.800000\n",
      "Month=1346, Predicted=4.795178, Expected=2.600000\n",
      "Month=1347, Predicted=4.626000, Expected=3.100000\n",
      "Month=1348, Predicted=4.850381, Expected=17.300000\n",
      "Month=1349, Predicted=13.146859, Expected=5.200000\n",
      "Month=1350, Predicted=8.511202, Expected=11.400000\n",
      "Month=1351, Predicted=11.168768, Expected=5.400000\n",
      "Month=1352, Predicted=8.524758, Expected=7.700000\n",
      "Month=1353, Predicted=9.047050, Expected=12.700000\n",
      "Month=1354, Predicted=12.567099, Expected=8.200000\n",
      "Month=1355, Predicted=11.072950, Expected=16.400000\n",
      "Month=1356, Predicted=15.325442, Expected=22.300000\n",
      "Month=1357, Predicted=21.521232, Expected=23.000000\n",
      "Month=1358, Predicted=24.413729, Expected=42.300000\n",
      "Month=1359, Predicted=35.819008, Expected=38.800000\n",
      "Month=1360, Predicted=39.648411, Expected=41.300000\n",
      "Month=1361, Predicted=42.507903, Expected=33.000000\n",
      "Month=1362, Predicted=37.324140, Expected=68.800000\n",
      "Month=1363, Predicted=50.548007, Expected=71.600000\n",
      "Month=1364, Predicted=63.861015, Expected=69.600000\n",
      "Month=1365, Predicted=70.471365, Expected=49.500000\n",
      "Month=1366, Predicted=55.899717, Expected=53.500000\n",
      "Month=1367, Predicted=54.932129, Expected=42.500000\n",
      "Month=1368, Predicted=47.204331, Expected=34.500000\n",
      "Month=1369, Predicted=39.440201, Expected=45.300000\n",
      "Month=1370, Predicted=43.165700, Expected=55.400000\n",
      "Month=1371, Predicted=52.569465, Expected=67.000000\n",
      "Month=1372, Predicted=64.610123, Expected=71.800000\n",
      "Month=1373, Predicted=72.132974, Expected=74.500000\n",
      "Month=1374, Predicted=75.713267, Expected=67.700000\n",
      "Month=1375, Predicted=71.699724, Expected=53.500000\n",
      "Month=1376, Predicted=59.749298, Expected=35.200000\n",
      "Month=1377, Predicted=42.562546, Expected=45.100000\n",
      "Month=1378, Predicted=44.547465, Expected=50.700000\n",
      "Month=1379, Predicted=49.730560, Expected=65.600000\n",
      "Month=1380, Predicted=61.379094, Expected=53.000000\n",
      "Month=1381, Predicted=56.690707, Expected=74.700000\n",
      "Month=1382, Predicted=66.492584, Expected=71.900000\n",
      "Month=1383, Predicted=71.426256, Expected=94.800000\n",
      "Month=1384, Predicted=86.829206, Expected=74.700000\n",
      "Month=1385, Predicted=78.141115, Expected=114.100000\n",
      "Month=1386, Predicted=92.423098, Expected=114.900000\n",
      "Month=1387, Predicted=103.869172, Expected=119.800000\n",
      "Month=1388, Predicted=118.190555, Expected=154.500000\n",
      "Month=1389, Predicted=141.397970, Expected=129.400000\n",
      "Month=1390, Predicted=132.038144, Expected=72.200000\n",
      "Month=1391, Predicted=80.120654, Expected=96.400000\n",
      "Month=1392, Predicted=86.957443, Expected=129.300000\n",
      "Month=1393, Predicted=118.365121, Expected=96.000000\n",
      "Month=1394, Predicted=101.269125, Expected=65.300000\n",
      "Month=1395, Predicted=72.946467, Expected=72.200000\n",
      "Month=1396, Predicted=72.651426, Expected=80.500000\n",
      "Month=1397, Predicted=78.431365, Expected=76.700000\n",
      "Month=1398, Predicted=78.886331, Expected=59.400000\n",
      "Month=1399, Predicted=65.727300, Expected=107.600000\n",
      "Month=1400, Predicted=78.679685, Expected=101.700000\n",
      "Month=1401, Predicted=83.670167, Expected=79.900000\n",
      "Month=1402, Predicted=77.963286, Expected=85.000000\n",
      "Month=1403, Predicted=83.625144, Expected=83.400000\n",
      "Month=1404, Predicted=85.284316, Expected=59.200000\n",
      "Month=1405, Predicted=66.022642, Expected=48.100000\n",
      "Month=1406, Predicted=54.264557, Expected=79.500000\n",
      "Month=1407, Predicted=64.734522, Expected=66.500000\n",
      "Month=1408, Predicted=63.519938, Expected=51.800000\n",
      "Month=1409, Predicted=55.721753, Expected=88.100000\n",
      "Month=1410, Predicted=69.045462, Expected=111.200000\n",
      "Month=1411, Predicted=104.175721, Expected=64.700000\n",
      "Month=1412, Predicted=72.214086, Expected=69.000000\n",
      "Month=1413, Predicted=70.098672, Expected=54.700000\n",
      "Month=1414, Predicted=59.896275, Expected=52.800000\n",
      "Month=1415, Predicted=55.995758, Expected=42.000000\n",
      "Month=1416, Predicted=47.187119, Expected=34.900000\n",
      "Month=1417, Predicted=39.726764, Expected=51.100000\n",
      "Month=1418, Predicted=46.044546, Expected=53.900000\n",
      "Month=1419, Predicted=53.046514, Expected=70.200000\n",
      "Month=1420, Predicted=65.757711, Expected=14.800000\n",
      "Month=1421, Predicted=22.720654, Expected=33.300000\n",
      "Month=1422, Predicted=26.691170, Expected=38.700000\n",
      "Month=1423, Predicted=35.885755, Expected=27.500000\n",
      "Month=1424, Predicted=31.495093, Expected=19.200000\n",
      "Month=1425, Predicted=24.170222, Expected=36.300000\n",
      "Month=1426, Predicted=30.862551, Expected=49.600000\n",
      "Month=1427, Predicted=45.465514, Expected=27.200000\n",
      "Month=1428, Predicted=32.516103, Expected=29.900000\n",
      "Month=1429, Predicted=31.368358, Expected=31.500000\n",
      "Month=1430, Predicted=32.462029, Expected=28.300000\n",
      "Month=1431, Predicted=30.989460, Expected=26.700000\n",
      "Month=1432, Predicted=29.329236, Expected=32.400000\n",
      "Month=1433, Predicted=32.223237, Expected=22.200000\n",
      "Month=1434, Predicted=26.425068, Expected=33.700000\n",
      "Month=1435, Predicted=31.179737, Expected=41.900000\n",
      "Month=1436, Predicted=39.898128, Expected=22.800000\n",
      "Month=1437, Predicted=28.169686, Expected=17.800000\n",
      "Month=1438, Predicted=22.029982, Expected=18.200000\n",
      "Month=1439, Predicted=20.318611, Expected=17.800000\n",
      "Month=1440, Predicted=19.706059, Expected=20.300000\n",
      "Month=1441, Predicted=21.239173, Expected=11.800000\n",
      "Month=1442, Predicted=15.968103, Expected=26.400000\n",
      "Month=1443, Predicted=22.267466, Expected=54.700000\n",
      "Month=1444, Predicted=44.039789, Expected=11.000000\n",
      "Month=1445, Predicted=17.426939, Expected=8.000000\n",
      "Month=1446, Predicted=11.219348, Expected=5.800000\n",
      "Month=1447, Predicted=8.326022, Expected=10.900000\n",
      "Month=1448, Predicted=10.790938, Expected=6.500000\n",
      "Month=1449, Predicted=9.232960, Expected=4.700000\n",
      "Month=1450, Predicted=7.427034, Expected=6.200000\n",
      "Month=1451, Predicted=7.694284, Expected=7.400000\n",
      "Month=1452, Predicted=8.731607, Expected=17.500000\n",
      "Month=1453, Predicted=15.311294, Expected=4.500000\n",
      "Month=1454, Predicted=8.771870, Expected=1.500000\n",
      "Month=1455, Predicted=4.926051, Expected=3.300000\n",
      "Month=1456, Predicted=4.752255, Expected=6.100000\n",
      "Month=1457, Predicted=6.769482, Expected=3.200000\n",
      "Month=1458, Predicted=5.770608, Expected=9.100000\n",
      "Month=1459, Predicted=8.936203, Expected=3.500000\n",
      "Month=1460, Predicted=6.604455, Expected=0.500000\n",
      "Month=1461, Predicted=3.699379, Expected=13.200000\n",
      "Month=1462, Predicted=9.859689, Expected=11.600000\n",
      "Month=1463, Predicted=12.662209, Expected=10.000000\n",
      "Month=1464, Predicted=12.477500, Expected=2.800000\n",
      "Month=1465, Predicted=7.103645, Expected=0.500000\n",
      "Month=1466, Predicted=3.704659, Expected=5.100000\n",
      "Month=1467, Predicted=5.393108, Expected=1.800000\n",
      "Month=1468, Predicted=4.278298, Expected=11.300000\n",
      "Month=1469, Predicted=9.530827, Expected=20.800000\n",
      "Month=1470, Predicted=18.628287, Expected=24.000000\n",
      "Month=1471, Predicted=24.549907, Expected=28.100000\n",
      "Month=1472, Predicted=28.737274, Expected=19.300000\n",
      "Month=1473, Predicted=23.631501, Expected=25.100000\n",
      "Month=1474, Predicted=25.311758, Expected=25.600000\n",
      "Month=1475, Predicted=26.807138, Expected=22.500000\n",
      "Month=1476, Predicted=25.309873, Expected=16.500000\n",
      "Month=1477, Predicted=20.513546, Expected=5.500000\n",
      "Month=1478, Predicted=11.032701, Expected=23.200000\n",
      "Month=1479, Predicted=17.527959, Expected=18.000000\n",
      "Month=1480, Predicted=18.822362, Expected=31.700000\n",
      "Month=1481, Predicted=27.982438, Expected=42.800000\n",
      "Month=1482, Predicted=40.333306, Expected=47.500000\n",
      "Month=1483, Predicted=47.903429, Expected=38.500000\n",
      "Month=1484, Predicted=43.045228, Expected=37.900000\n",
      "Month=1485, Predicted=40.701827, Expected=60.200000\n",
      "Month=1486, Predicted=51.321777, Expected=69.200000\n",
      "Month=1487, Predicted=66.371671, Expected=58.600000\n",
      "Month=1488, Predicted=62.878883, Expected=98.600000\n",
      "Month=1489, Predicted=77.305631, Expected=71.800000\n",
      "Month=1490, Predicted=69.319668, Expected=70.000000\n",
      "Month=1491, Predicted=70.482620, Expected=62.500000\n",
      "Month=1492, Predicted=66.302425, Expected=38.500000\n",
      "Month=1493, Predicted=45.641136, Expected=64.300000\n",
      "Month=1494, Predicted=53.854279, Expected=73.500000\n",
      "Month=1495, Predicted=69.199970, Expected=52.300000\n",
      "Month=1496, Predicted=57.500339, Expected=61.600000\n",
      "Month=1497, Predicted=60.210529, Expected=60.800000\n",
      "Month=1498, Predicted=61.913683, Expected=71.500000\n",
      "Month=1499, Predicted=69.152890, Expected=60.500000\n",
      "Month=1500, Predicted=64.359367, Expected=79.400000\n",
      "Month=1501, Predicted=72.871362, Expected=81.600000\n",
      "Month=1502, Predicted=80.708186, Expected=93.000000\n",
      "Month=1503, Predicted=90.850693, Expected=69.600000\n",
      "Month=1504, Predicted=75.455000, Expected=93.500000\n",
      "Month=1505, Predicted=83.651230, Expected=79.100000\n",
      "Month=1506, Predicted=79.499182, Expected=59.100000\n",
      "Month=1507, Predicted=64.930830, Expected=54.900000\n",
      "Month=1508, Predicted=58.916111, Expected=53.800000\n",
      "Month=1509, Predicted=56.354187, Expected=68.400000\n",
      "Month=1510, Predicted=63.852149, Expected=63.100000\n",
      "Month=1511, Predicted=64.728483, Expected=67.200000\n",
      "Month=1512, Predicted=67.750113, Expected=45.200000\n",
      "Month=1513, Predicted=51.466583, Expected=83.500000\n",
      "Month=1514, Predicted=62.895798, Expected=73.500000\n",
      "Month=1515, Predicted=64.979866, Expected=85.400000\n",
      "Month=1516, Predicted=81.575701, Expected=80.600000\n",
      "Month=1517, Predicted=83.513645, Expected=76.900000\n",
      "Month=1518, Predicted=80.566905, Expected=91.400000\n",
      "Month=1519, Predicted=87.304523, Expected=98.000000\n",
      "Month=1520, Predicted=96.461338, Expected=83.800000\n",
      "Month=1521, Predicted=88.810529, Expected=89.700000\n",
      "Month=1522, Predicted=90.035350, Expected=61.400000\n",
      "Month=1523, Predicted=68.118165, Expected=50.300000\n",
      "Month=1524, Predicted=56.270075, Expected=59.000000\n",
      "Month=1525, Predicted=58.120087, Expected=68.900000\n",
      "Month=1526, Predicted=66.127656, Expected=64.100000\n",
      "Month=1527, Predicted=66.516398, Expected=50.200000\n",
      "Month=1528, Predicted=56.098915, Expected=52.800000\n",
      "Month=1529, Predicted=54.706446, Expected=58.200000\n",
      "Month=1530, Predicted=57.809368, Expected=71.900000\n",
      "Month=1531, Predicted=67.916697, Expected=70.200000\n",
      "Month=1532, Predicted=71.604480, Expected=65.800000\n",
      "Month=1533, Predicted=69.294894, Expected=34.400000\n",
      "Month=1534, Predicted=41.939883, Expected=54.000000\n",
      "Month=1535, Predicted=47.557768, Expected=81.100000\n",
      "Month=1536, Predicted=71.135909, Expected=108.000000\n",
      "Month=1537, Predicted=104.847144, Expected=65.300000\n",
      "Month=1538, Predicted=72.960612, Expected=49.200000\n",
      "Month=1539, Predicted=56.366371, Expected=35.000000\n",
      "Month=1540, Predicted=41.985772, Expected=38.200000\n",
      "Month=1541, Predicted=40.318602, Expected=36.800000\n",
      "Month=1542, Predicted=38.981675, Expected=28.800000\n",
      "Month=1543, Predicted=33.112033, Expected=21.900000\n",
      "Month=1544, Predicted=26.472129, Expected=24.900000\n",
      "Month=1545, Predicted=26.173878, Expected=32.100000\n",
      "Month=1546, Predicted=30.899715, Expected=34.400000\n",
      "Month=1547, Predicted=34.950867, Expected=35.600000\n",
      "Month=1548, Predicted=37.062017, Expected=25.800000\n",
      "Month=1549, Predicted=30.535528, Expected=14.600000\n",
      "Month=1550, Predicted=20.384627, Expected=43.100000\n",
      "Month=1551, Predicted=30.430018, Expected=30.000000\n",
      "Month=1552, Predicted=28.480267, Expected=31.200000\n",
      "Month=1553, Predicted=31.659858, Expected=24.600000\n",
      "Month=1554, Predicted=28.289827, Expected=15.300000\n",
      "Month=1555, Predicted=20.414103, Expected=17.400000\n",
      "Month=1556, Predicted=19.217972, Expected=13.000000\n",
      "Month=1557, Predicted=16.104714, Expected=19.000000\n",
      "Month=1558, Predicted=18.760886, Expected=10.000000\n",
      "Month=1559, Predicted=13.889796, Expected=18.700000\n",
      "Month=1560, Predicted=17.470733, Expected=17.800000\n",
      "Month=1561, Predicted=19.148602, Expected=12.100000\n",
      "Month=1562, Predicted=15.754731, Expected=10.600000\n",
      "Month=1563, Predicted=13.423413, Expected=11.200000\n",
      "Month=1564, Predicted=12.992556, Expected=11.200000\n",
      "Month=1565, Predicted=12.994559, Expected=17.900000\n",
      "Month=1566, Predicted=17.207450, Expected=22.200000\n",
      "Month=1567, Predicted=22.144088, Expected=9.600000\n",
      "Month=1568, Predicted=14.580770, Expected=6.800000\n",
      "Month=1569, Predicted=10.374162, Expected=4.000000\n",
      "Month=1570, Predicted=7.089016, Expected=8.900000\n",
      "Month=1571, Predicted=9.051964, Expected=8.200000\n",
      "Month=1572, Predicted=9.846522, Expected=11.000000\n",
      "Month=1573, Predicted=11.919795, Expected=12.300000\n",
      "Month=1574, Predicted=13.595293, Expected=22.200000\n",
      "Month=1575, Predicted=20.183090, Expected=10.100000\n",
      "Month=1576, Predicted=14.270776, Expected=2.900000\n",
      "Month=1577, Predicted=7.558597, Expected=3.200000\n",
      "Month=1578, Predicted=5.540775, Expected=5.200000\n",
      "Month=1579, Predicted=6.288234, Expected=2.800000\n",
      "Month=1580, Predicted=5.239081, Expected=0.200000\n",
      "Month=1581, Predicted=3.088664, Expected=5.100000\n",
      "Month=1582, Predicted=5.311208, Expected=3.000000\n",
      "Month=1583, Predicted=5.141215, Expected=0.600000\n",
      "Month=1584, Predicted=3.399661, Expected=0.300000\n",
      "Month=1585, Predicted=2.484809, Expected=3.400000\n",
      "Month=1586, Predicted=4.167579, Expected=7.800000\n",
      "Month=1587, Predicted=7.861997, Expected=4.300000\n",
      "Month=1588, Predicted=6.988426, Expected=11.300000\n",
      "Month=1589, Predicted=10.740040, Expected=19.700000\n",
      "Month=1590, Predicted=18.035628, Expected=6.700000\n",
      "Month=1591, Predicted=11.276160, Expected=9.300000\n",
      "Month=1592, Predicted=10.849912, Expected=8.300000\n",
      "Month=1593, Predicted=10.298122, Expected=4.000000\n",
      "Month=1594, Predicted=7.274452, Expected=5.700000\n",
      "Month=1595, Predicted=7.249740, Expected=8.700000\n",
      "Month=1596, Predicted=9.349223, Expected=15.400000\n",
      "Month=1597, Predicted=14.589141, Expected=18.900000\n",
      "Month=1598, Predicted=19.239979, Expected=20.500000\n",
      "Month=1599, Predicted=21.807287, Expected=23.100000\n",
      "Month=1600, Predicted=24.138661, Expected=12.200000\n",
      "Month=1601, Predicted=17.035606, Expected=27.300000\n",
      "Month=1602, Predicted=23.023555, Expected=45.700000\n",
      "Month=1603, Predicted=39.588765, Expected=33.900000\n",
      "Month=1604, Predicted=36.974202, Expected=30.100000\n",
      "Month=1605, Predicted=33.624297, Expected=42.100000\n",
      "Month=1606, Predicted=39.190960, Expected=53.200000\n",
      "Month=1607, Predicted=50.178823, Expected=64.200000\n",
      "Month=1608, Predicted=62.246768, Expected=61.500000\n",
      "Month=1609, Predicted=64.070623, Expected=62.800000\n",
      "Month=1610, Predicted=64.693140, Expected=74.300000\n",
      "Month=1611, Predicted=71.539704, Expected=77.100000\n",
      "Month=1612, Predicted=77.233800, Expected=74.900000\n",
      "Month=1613, Predicted=77.473168, Expected=54.600000\n",
      "Month=1614, Predicted=61.265563, Expected=70.000000\n",
      "Month=1615, Predicted=65.965613, Expected=52.300000\n",
      "Month=1616, Predicted=56.194964, Expected=87.000000\n",
      "Month=1617, Predicted=68.888336, Expected=76.000000\n",
      "Month=1618, Predicted=70.350311, Expected=89.000000\n",
      "Month=1619, Predicted=85.161964, Expected=115.400000\n",
      "Month=1620, Predicted=107.855448, Expected=123.400000\n",
      "Month=1621, Predicted=123.274230, Expected=132.500000\n",
      "Month=1622, Predicted=132.039337, Expected=128.500000\n",
      "Month=1623, Predicted=131.564654, Expected=83.900000\n",
      "Month=1624, Predicted=91.820654, Expected=109.300000\n",
      "Month=1625, Predicted=99.099519, Expected=116.700000\n",
      "Month=1626, Predicted=112.552623, Expected=130.300000\n",
      "Month=1627, Predicted=127.966146, Expected=145.100000\n",
      "Month=1628, Predicted=142.297789, Expected=137.700000\n",
      "Month=1629, Predicted=141.218889, Expected=100.700000\n",
      "Month=1630, Predicted=108.536887, Expected=124.900000\n",
      "Month=1631, Predicted=115.558533, Expected=74.400000\n",
      "Month=1632, Predicted=81.705350, Expected=88.800000\n",
      "Month=1633, Predicted=83.296292, Expected=98.400000\n",
      "Month=1634, Predicted=94.208243, Expected=119.200000\n",
      "Month=1635, Predicted=113.579919, Expected=86.500000\n",
      "Month=1636, Predicted=92.741025, Expected=101.000000\n",
      "Month=1637, Predicted=96.705472, Expected=127.400000\n",
      "Month=1638, Predicted=116.978531, Expected=97.500000\n",
      "Month=1639, Predicted=101.946127, Expected=165.300000\n",
      "Month=1640, Predicted=114.941840, Expected=115.700000\n",
      "Month=1641, Predicted=99.720683, Expected=89.600000\n",
      "Month=1642, Predicted=88.077138, Expected=99.100000\n",
      "Month=1643, Predicted=94.802494, Expected=122.200000\n",
      "Month=1644, Predicted=114.576327, Expected=92.700000\n",
      "Month=1645, Predicted=98.001562, Expected=80.300000\n",
      "Month=1646, Predicted=86.212974, Expected=77.400000\n",
      "Month=1647, Predicted=81.143833, Expected=64.600000\n",
      "Month=1648, Predicted=70.371220, Expected=109.100000\n",
      "Month=1649, Predicted=83.333599, Expected=118.300000\n",
      "Month=1650, Predicted=102.321550, Expected=101.000000\n",
      "Month=1651, Predicted=100.678308, Expected=97.600000\n",
      "Month=1652, Predicted=100.055354, Expected=105.800000\n",
      "Month=1653, Predicted=104.674973, Expected=112.600000\n",
      "Month=1654, Predicted=111.533596, Expected=88.100000\n",
      "Month=1655, Predicted=94.287138, Expected=68.100000\n",
      "Month=1656, Predicted=75.407522, Expected=42.100000\n",
      "Month=1657, Predicted=49.885195, Expected=50.500000\n",
      "Month=1658, Predicted=50.920828, Expected=59.400000\n",
      "Month=1659, Predicted=57.247464, Expected=83.300000\n",
      "Month=1660, Predicted=74.788467, Expected=60.700000\n",
      "Month=1661, Predicted=64.501777, Expected=54.400000\n",
      "Month=1662, Predicted=58.489040, Expected=83.900000\n",
      "Month=1663, Predicted=70.104011, Expected=67.500000\n",
      "Month=1664, Predicted=66.430166, Expected=105.500000\n",
      "Month=1665, Predicted=86.495067, Expected=66.500000\n",
      "Month=1666, Predicted=69.269341, Expected=55.000000\n",
      "Month=1667, Predicted=59.665152, Expected=58.400000\n",
      "Month=1668, Predicted=59.338640, Expected=68.300000\n",
      "Month=1669, Predicted=65.798611, Expected=45.600000\n",
      "Month=1670, Predicted=51.075877, Expected=44.500000\n",
      "Month=1671, Predicted=47.312427, Expected=46.400000\n",
      "Month=1672, Predicted=47.526884, Expected=32.800000\n",
      "Month=1673, Predicted=38.096434, Expected=29.500000\n",
      "Month=1674, Predicted=33.254463, Expected=59.800000\n",
      "Month=1675, Predicted=45.403294, Expected=66.900000\n",
      "Month=1676, Predicted=61.956169, Expected=60.000000\n",
      "Month=1677, Predicted=63.019874, Expected=65.900000\n",
      "Month=1678, Predicted=66.179988, Expected=46.300000\n",
      "Month=1679, Predicted=52.224901, Expected=38.300000\n",
      "Month=1680, Predicted=43.495725, Expected=33.700000\n",
      "Month=1681, Predicted=37.772418, Expected=35.600000\n",
      "Month=1682, Predicted=37.119844, Expected=52.800000\n",
      "Month=1683, Predicted=46.813165, Expected=54.200000\n",
      "Month=1684, Predicted=53.991036, Expected=60.700000\n",
      "Month=1685, Predicted=60.492849, Expected=25.000000\n",
      "Month=1686, Predicted=32.366211, Expected=11.400000\n",
      "Month=1687, Predicted=18.014716, Expected=17.700000\n",
      "Month=1688, Predicted=18.215721, Expected=20.200000\n",
      "Month=1689, Predicted=20.576446, Expected=17.200000\n",
      "Month=1690, Predicted=19.746346, Expected=19.200000\n",
      "Month=1691, Predicted=20.580582, Expected=30.700000\n",
      "Month=1692, Predicted=27.821402, Expected=22.500000\n",
      "Month=1693, Predicted=25.530223, Expected=12.400000\n",
      "Month=1694, Predicted=17.570768, Expected=28.900000\n",
      "Month=1695, Predicted=23.882041, Expected=27.400000\n",
      "Month=1696, Predicted=27.670360, Expected=26.100000\n",
      "Month=1697, Predicted=28.344379, Expected=14.100000\n",
      "Month=1698, Predicted=19.529545, Expected=7.600000\n",
      "Month=1699, Predicted=12.384505, Expected=13.200000\n",
      "Month=1700, Predicted=13.436036, Expected=19.400000\n",
      "Month=1701, Predicted=18.426706, Expected=10.000000\n",
      "Month=1702, Predicted=13.928795, Expected=7.800000\n",
      "Month=1703, Predicted=10.934591, Expected=10.200000\n",
      "Month=1704, Predicted=11.384903, Expected=18.800000\n",
      "Month=1705, Predicted=17.108575, Expected=3.700000\n",
      "Month=1706, Predicted=8.472621, Expected=0.500000\n",
      "Month=1707, Predicted=4.069703, Expected=11.000000\n",
      "Month=1708, Predicted=8.684216, Expected=0.300000\n",
      "Month=1709, Predicted=3.841421, Expected=2.500000\n",
      "Month=1710, Predicted=3.917567, Expected=5.000000\n",
      "Month=1711, Predicted=5.791111, Expected=5.000000\n",
      "Month=1712, Predicted=6.680690, Expected=16.700000\n",
      "Month=1713, Predicted=13.873393, Expected=14.300000\n",
      "Month=1714, Predicted=15.939240, Expected=16.900000\n",
      "Month=1715, Predicted=18.073341, Expected=10.800000\n",
      "Month=1716, Predicted=14.477787, Expected=28.400000\n",
      "Month=1717, Predicted=22.581843, Expected=18.500000\n",
      "Month=1718, Predicted=20.453200, Expected=12.700000\n",
      "Month=1719, Predicted=16.424636, Expected=21.500000\n",
      "Month=1720, Predicted=20.177616, Expected=32.000000\n",
      "Month=1721, Predicted=29.253833, Expected=30.600000\n",
      "Month=1722, Predicted=32.281717, Expected=36.200000\n",
      "Month=1723, Predicted=36.329248, Expected=42.600000\n",
      "Month=1724, Predicted=41.976562, Expected=25.900000\n",
      "Month=1725, Predicted=31.326990, Expected=34.900000\n",
      "Month=1726, Predicted=33.795874, Expected=68.800000\n",
      "Month=1727, Predicted=52.929675, Expected=46.000000\n",
      "Month=1728, Predicted=46.404515, Expected=27.400000\n",
      "Month=1729, Predicted=33.034495, Expected=47.600000\n",
      "Month=1730, Predicted=40.145197, Expected=86.200000\n",
      "Month=1731, Predicted=72.044977, Expected=76.600000\n",
      "Month=1732, Predicted=76.314019, Expected=75.700000\n",
      "Month=1733, Predicted=77.893638, Expected=84.900000\n",
      "Month=1734, Predicted=83.466131, Expected=73.500000\n",
      "Month=1735, Predicted=77.681722, Expected=116.200000\n",
      "Month=1736, Predicted=92.162238, Expected=107.200000\n",
      "Month=1737, Predicted=96.077673, Expected=94.400000\n",
      "Month=1738, Predicted=94.123320, Expected=102.300000\n",
      "Month=1739, Predicted=100.661837, Expected=123.800000\n",
      "Month=1740, Predicted=116.558784, Expected=121.700000\n",
      "Month=1741, Predicted=122.579516, Expected=115.700000\n",
      "Month=1742, Predicted=119.656394, Expected=113.400000\n",
      "Month=1743, Predicted=116.645123, Expected=129.800000\n",
      "Month=1744, Predicted=124.472754, Expected=149.800000\n",
      "Month=1745, Predicted=143.554378, Expected=201.300000\n",
      "Month=1746, Predicted=183.214781, Expected=163.900000\n",
      "Month=1747, Predicted=167.799210, Expected=157.900000\n",
      "Month=1748, Predicted=161.751092, Expected=188.800000\n",
      "Month=1749, Predicted=173.862420, Expected=169.400000\n",
      "Month=1750, Predicted=168.495255, Expected=163.600000\n",
      "Month=1751, Predicted=166.092330, Expected=128.000000\n",
      "Month=1752, Predicted=135.654818, Expected=116.500000\n",
      "Month=1753, Predicted=122.815980, Expected=108.500000\n",
      "Month=1754, Predicted=113.859586, Expected=86.100000\n",
      "Month=1755, Predicted=93.416012, Expected=94.800000\n",
      "Month=1756, Predicted=94.575564, Expected=189.700000\n",
      "Month=1757, Predicted=120.503138, Expected=174.000000\n",
      "Month=1758, Predicted=118.227317, Expected=167.800000\n",
      "Month=1759, Predicted=118.879074, Expected=142.200000\n",
      "Month=1760, Predicted=114.899033, Expected=157.900000\n",
      "Month=1761, Predicted=139.964940, Expected=143.300000\n",
      "Month=1762, Predicted=141.835553, Expected=136.300000\n",
      "Month=1763, Predicted=139.622538, Expected=95.800000\n",
      "Month=1764, Predicted=103.720654, Expected=138.000000\n",
      "Month=1765, Predicted=114.391888, Expected=119.100000\n",
      "Month=1766, Predicted=111.205592, Expected=182.300000\n",
      "Month=1767, Predicted=152.457762, Expected=157.500000\n",
      "Month=1768, Predicted=152.704804, Expected=147.000000\n",
      "Month=1769, Predicted=149.746675, Expected=106.200000\n",
      "Month=1770, Predicted=114.120654, Expected=121.700000\n",
      "Month=1771, Predicted=117.560277, Expected=125.800000\n",
      "Month=1772, Predicted=124.283551, Expected=123.800000\n",
      "Month=1773, Predicted=125.904024, Expected=145.300000\n",
      "Month=1774, Predicted=137.521359, Expected=131.600000\n",
      "Month=1775, Predicted=133.573878, Expected=143.500000\n",
      "Month=1776, Predicted=140.364365, Expected=117.600000\n",
      "Month=1777, Predicted=123.265798, Expected=101.600000\n",
      "Month=1778, Predicted=108.290672, Expected=94.800000\n",
      "Month=1779, Predicted=99.990287, Expected=109.700000\n",
      "Month=1780, Predicted=105.449464, Expected=113.400000\n",
      "Month=1781, Predicted=112.434879, Expected=106.200000\n",
      "Month=1782, Predicted=109.854697, Expected=83.600000\n",
      "Month=1783, Predicted=90.662067, Expected=91.000000\n",
      "Month=1784, Predicted=91.180742, Expected=85.200000\n",
      "Month=1785, Predicted=88.147168, Expected=51.300000\n",
      "Month=1786, Predicted=58.902768, Expected=61.400000\n",
      "Month=1787, Predicted=60.116326, Expected=54.800000\n",
      "Month=1788, Predicted=57.381421, Expected=54.100000\n",
      "Month=1789, Predicted=56.334186, Expected=59.900000\n",
      "Month=1790, Predicted=59.601922, Expected=59.900000\n",
      "Month=1791, Predicted=61.316520, Expected=59.900000\n",
      "Month=1792, Predicted=61.822346, Expected=92.900000\n",
      "Month=1793, Predicted=77.223690, Expected=108.500000\n",
      "Month=1794, Predicted=103.681387, Expected=100.600000\n",
      "Month=1795, Predicted=104.447979, Expected=61.500000\n",
      "Month=1796, Predicted=69.420654, Expected=61.000000\n",
      "Month=1797, Predicted=64.523064, Expected=83.100000\n",
      "Month=1798, Predicted=74.080336, Expected=51.600000\n",
      "Month=1799, Predicted=56.154395, Expected=52.400000\n",
      "Month=1800, Predicted=53.740622, Expected=45.800000\n",
      "Month=1801, Predicted=49.256063, Expected=40.700000\n",
      "Month=1802, Predicted=44.506432, Expected=22.700000\n",
      "Month=1803, Predicted=29.401929, Expected=22.000000\n",
      "Month=1804, Predicted=25.348598, Expected=29.100000\n",
      "Month=1805, Predicted=28.250555, Expected=23.400000\n",
      "Month=1806, Predicted=26.218536, Expected=36.400000\n",
      "Month=1807, Predicted=32.994263, Expected=39.300000\n",
      "Month=1808, Predicted=39.154813, Expected=54.900000\n",
      "Month=1809, Predicted=50.665794, Expected=28.200000\n",
      "Month=1810, Predicted=33.833954, Expected=23.800000\n",
      "Month=1811, Predicted=27.684023, Expected=22.100000\n",
      "Month=1812, Predicted=24.793251, Expected=34.300000\n",
      "Month=1813, Predicted=30.996403, Expected=26.500000\n",
      "Month=1814, Predicted=29.120906, Expected=3.900000\n",
      "Month=1815, Predicted=10.718170, Expected=10.000000\n",
      "Month=1816, Predicted=10.580837, Expected=27.800000\n",
      "Month=1817, Predicted=21.218630, Expected=12.500000\n",
      "Month=1818, Predicted=15.361031, Expected=21.800000\n",
      "Month=1819, Predicted=19.949140, Expected=8.600000\n",
      "Month=1820, Predicted=12.883650, Expected=23.500000\n",
      "Month=1821, Predicted=19.146532, Expected=19.300000\n",
      "Month=1822, Predicted=20.559587, Expected=8.200000\n",
      "Month=1823, Predicted=13.196410, Expected=1.600000\n",
      "Month=1824, Predicted=6.308379, Expected=2.500000\n",
      "Month=1825, Predicted=4.614607, Expected=0.200000\n",
      "Month=1826, Predicted=2.732571, Expected=0.500000\n",
      "Month=1827, Predicted=2.360363, Expected=10.900000\n",
      "Month=1828, Predicted=8.530619, Expected=1.800000\n",
      "Month=1829, Predicted=5.143680, Expected=0.800000\n",
      "Month=1830, Predicted=3.404443, Expected=0.200000\n",
      "Month=1831, Predicted=2.385950, Expected=4.800000\n",
      "Month=1832, Predicted=4.975676, Expected=8.400000\n",
      "Month=1833, Predicted=8.669047, Expected=1.500000\n",
      "Month=1834, Predicted=5.201670, Expected=7.000000\n",
      "Month=1835, Predicted=7.216870, Expected=9.200000\n",
      "Month=1836, Predicted=9.876698, Expected=7.600000\n",
      "Month=1837, Predicted=9.857444, Expected=23.100000\n",
      "Month=1838, Predicted=18.425762, Expected=20.800000\n",
      "Month=1839, Predicted=21.818670, Expected=4.900000\n",
      "Month=1840, Predicted=10.827924, Expected=11.300000\n",
      "Month=1841, Predicted=11.634703, Expected=28.900000\n",
      "Month=1842, Predicted=22.578369, Expected=31.700000\n",
      "Month=1843, Predicted=31.269195, Expected=26.700000\n",
      "Month=1844, Predicted=30.145242, Expected=40.700000\n",
      "Month=1845, Predicted=37.068579, Expected=42.700000\n",
      "Month=1846, Predicted=42.739845, Expected=58.500000\n",
      "Month=1847, Predicted=54.133042, Expected=89.200000\n",
      "Month=1848, Predicted=78.844653, Expected=76.900000\n",
      "Month=1849, Predicted=78.550968, Expected=73.600000\n",
      "Month=1850, Predicted=76.707539, Expected=124.000000\n",
      "Month=1851, Predicted=93.346654, Expected=118.400000\n",
      "Month=1852, Predicted=99.858302, Expected=110.700000\n",
      "Month=1853, Predicted=104.237261, Expected=136.600000\n",
      "Month=1854, Predicted=128.807149, Expected=116.600000\n",
      "Month=1855, Predicted=120.735545, Expected=129.100000\n",
      "Month=1856, Predicted=126.014219, Expected=169.600000\n",
      "Month=1857, Predicted=150.823612, Expected=173.200000\n",
      "Month=1858, Predicted=168.195043, Expected=155.300000\n",
      "Month=1859, Predicted=160.021374, Expected=201.300000\n",
      "Month=1860, Predicted=174.304152, Expected=192.100000\n",
      "Month=1861, Predicted=178.157173, Expected=165.000000\n",
      "Month=1862, Predicted=166.655903, Expected=130.200000\n",
      "Month=1863, Predicted=137.616410, Expected=157.400000\n",
      "Month=1864, Predicted=144.943142, Expected=175.200000\n",
      "Month=1865, Predicted=168.369682, Expected=164.600000\n",
      "Month=1866, Predicted=167.786320, Expected=200.700000\n",
      "Month=1867, Predicted=182.932285, Expected=187.200000\n",
      "Month=1868, Predicted=183.114906, Expected=158.000000\n",
      "Month=1869, Predicted=163.738240, Expected=235.800000\n",
      "Month=1870, Predicted=175.896186, Expected=253.800000\n",
      "Month=1871, Predicted=180.625713, Expected=210.900000\n",
      "Month=1872, Predicted=168.583769, Expected=239.400000\n",
      "Month=1873, Predicted=198.093699, Expected=202.500000\n",
      "Month=1874, Predicted=193.794079, Expected=164.900000\n",
      "Month=1875, Predicted=170.511728, Expected=190.700000\n",
      "Month=1876, Predicted=177.943400, Expected=196.000000\n",
      "Month=1877, Predicted=190.905213, Expected=175.300000\n",
      "Month=1878, Predicted=180.069234, Expected=171.500000\n",
      "Month=1879, Predicted=175.175930, Expected=191.400000\n",
      "Month=1880, Predicted=183.938786, Expected=200.200000\n",
      "Month=1881, Predicted=197.428915, Expected=201.200000\n",
      "Month=1882, Predicted=202.796468, Expected=181.500000\n",
      "Month=1883, Predicted=188.004637, Expected=152.300000\n",
      "Month=1884, Predicted=160.060983, Expected=187.600000\n",
      "Month=1885, Predicted=170.731343, Expected=217.400000\n",
      "Month=1886, Predicted=209.935471, Expected=143.100000\n",
      "Month=1887, Predicted=151.020654, Expected=185.700000\n",
      "Month=1888, Predicted=161.686335, Expected=163.300000\n",
      "Month=1889, Predicted=156.450763, Expected=172.000000\n",
      "Month=1890, Predicted=168.042152, Expected=168.700000\n",
      "Month=1891, Predicted=170.807473, Expected=149.600000\n",
      "Month=1892, Predicted=156.143602, Expected=199.600000\n",
      "Month=1893, Predicted=169.018573, Expected=145.200000\n",
      "Month=1894, Predicted=145.849805, Expected=111.400000\n",
      "Month=1895, Predicted=118.318158, Expected=124.000000\n",
      "Month=1896, Predicted=120.013271, Expected=125.000000\n",
      "Month=1897, Predicted=124.245229, Expected=146.300000\n",
      "Month=1898, Predicted=138.920468, Expected=106.000000\n",
      "Month=1899, Predicted=112.580916, Expected=102.200000\n",
      "Month=1900, Predicted=105.773725, Expected=122.000000\n",
      "Month=1901, Predicted=114.186991, Expected=119.600000\n",
      "Month=1902, Predicted=119.058866, Expected=110.200000\n",
      "Month=1903, Predicted=114.437165, Expected=121.700000\n",
      "Month=1904, Predicted=119.306285, Expected=134.100000\n",
      "Month=1905, Predicted=130.507473, Expected=127.200000\n",
      "Month=1906, Predicted=130.083072, Expected=82.800000\n",
      "Month=1907, Predicted=90.720654, Expected=89.600000\n",
      "Month=1908, Predicted=90.067696, Expected=85.600000\n",
      "Month=1909, Predicted=88.000162, Expected=57.900000\n",
      "Month=1910, Predicted=65.009516, Expected=46.100000\n",
      "Month=1911, Predicted=52.419321, Expected=53.000000\n",
      "Month=1912, Predicted=53.145614, Expected=61.400000\n",
      "Month=1913, Predicted=59.388005, Expected=51.000000\n",
      "Month=1914, Predicted=54.821268, Expected=77.400000\n",
      "Month=1915, Predicted=66.120691, Expected=70.200000\n",
      "Month=1916, Predicted=68.598793, Expected=55.900000\n",
      "Month=1917, Predicted=60.618957, Expected=63.600000\n",
      "Month=1918, Predicted=62.966528, Expected=37.700000\n",
      "Month=1919, Predicted=43.943787, Expected=32.600000\n",
      "Month=1920, Predicted=36.861780, Expected=40.000000\n",
      "Month=1921, Predicted=39.145629, Expected=38.700000\n",
      "Month=1922, Predicted=40.157620, Expected=50.300000\n",
      "Month=1923, Predicted=47.528582, Expected=45.600000\n",
      "Month=1924, Predicted=47.870308, Expected=46.400000\n",
      "Month=1925, Predicted=48.279375, Expected=43.700000\n",
      "Month=1926, Predicted=46.499593, Expected=42.000000\n",
      "Month=1927, Predicted=44.661762, Expected=21.800000\n",
      "Month=1928, Predicted=28.392763, Expected=21.800000\n",
      "Month=1929, Predicted=24.770430, Expected=51.300000\n",
      "Month=1930, Predicted=37.355495, Expected=39.500000\n",
      "Month=1931, Predicted=37.247460, Expected=26.900000\n",
      "Month=1932, Predicted=30.875460, Expected=23.200000\n",
      "Month=1933, Predicted=26.734257, Expected=19.800000\n",
      "Month=1934, Predicted=23.090045, Expected=24.400000\n",
      "Month=1935, Predicted=24.725671, Expected=17.100000\n",
      "Month=1936, Predicted=20.703333, Expected=29.300000\n",
      "Month=1937, Predicted=26.330881, Expected=43.000000\n",
      "Month=1938, Predicted=38.945042, Expected=35.900000\n",
      "Month=1939, Predicted=38.766636, Expected=19.600000\n",
      "Month=1940, Predicted=26.063604, Expected=33.200000\n",
      "Month=1941, Predicted=30.252934, Expected=38.800000\n",
      "Month=1942, Predicted=37.411843, Expected=35.300000\n",
      "Month=1943, Predicted=37.863492, Expected=23.400000\n",
      "Month=1944, Predicted=28.927384, Expected=14.900000\n",
      "Month=1945, Predicted=20.245098, Expected=15.300000\n",
      "Month=1946, Predicted=17.785961, Expected=17.700000\n",
      "Month=1947, Predicted=18.632953, Expected=16.500000\n",
      "Month=1948, Predicted=18.503577, Expected=8.600000\n",
      "Month=1949, Predicted=12.919606, Expected=9.500000\n",
      "Month=1950, Predicted=11.590013, Expected=9.100000\n",
      "Month=1951, Predicted=11.027595, Expected=3.100000\n",
      "Month=1952, Predicted=6.827731, Expected=9.300000\n",
      "Month=1953, Predicted=9.125776, Expected=4.700000\n",
      "Month=1954, Predicted=7.418857, Expected=6.100000\n",
      "Month=1955, Predicted=7.703772, Expected=7.400000\n",
      "Month=1956, Predicted=8.737444, Expected=15.100000\n",
      "Month=1957, Predicted=13.958902, Expected=17.500000\n",
      "Month=1958, Predicted=18.089586, Expected=14.200000\n",
      "Month=1959, Predicted=17.089165, Expected=11.700000\n",
      "Month=1960, Predicted=14.737330, Expected=6.800000\n",
      "Month=1961, Predicted=10.496049, Expected=24.100000\n",
      "Month=1962, Predicted=18.321637, Expected=15.900000\n",
      "Month=1963, Predicted=17.517719, Expected=11.900000\n",
      "Month=1964, Predicted=15.076869, Expected=8.900000\n",
      "Month=1965, Predicted=12.085840, Expected=16.800000\n",
      "Month=1966, Predicted=15.737859, Expected=20.100000\n",
      "Month=1967, Predicted=20.169486, Expected=15.800000\n",
      "Month=1968, Predicted=18.817698, Expected=17.000000\n",
      "Month=1969, Predicted=18.809855, Expected=28.200000\n",
      "Month=1970, Predicted=25.468148, Expected=24.400000\n",
      "Month=1971, Predicted=26.379009, Expected=25.300000\n",
      "Month=1972, Predicted=27.090884, Expected=48.700000\n",
      "Month=1973, Predicted=39.473528, Expected=45.300000\n",
      "Month=1974, Predicted=44.808761, Expected=47.700000\n",
      "Month=1975, Predicted=48.776084, Expected=56.700000\n",
      "Month=1976, Predicted=55.308678, Expected=51.200000\n",
      "Month=1977, Predicted=54.135020, Expected=50.200000\n",
      "Month=1978, Predicted=52.789261, Expected=57.200000\n",
      "Month=1979, Predicted=56.481953, Expected=57.200000\n",
      "Month=1980, Predicted=58.504102, Expected=70.400000\n",
      "Month=1981, Predicted=66.946097, Expected=110.900000\n",
      "Month=1982, Predicted=93.447887, Expected=93.600000\n",
      "Month=1983, Predicted=92.565316, Expected=111.800000\n",
      "Month=1984, Predicted=105.778304, Expected=69.500000\n",
      "Month=1985, Predicted=76.565620, Expected=86.500000\n",
      "Month=1986, Predicted=80.375473, Expected=67.300000\n",
      "Month=1987, Predicted=70.331783, Expected=91.500000\n",
      "Month=1988, Predicted=80.674326, Expected=107.200000\n",
      "Month=1989, Predicted=102.477017, Expected=76.800000\n",
      "Month=1990, Predicted=83.114238, Expected=88.200000\n",
      "Month=1991, Predicted=85.829497, Expected=94.300000\n",
      "Month=1992, Predicted=92.693416, Expected=126.400000\n",
      "Month=1993, Predicted=113.283735, Expected=121.800000\n",
      "Month=1994, Predicted=120.219589, Expected=111.900000\n",
      "Month=1995, Predicted=116.089020, Expected=92.200000\n",
      "Month=1996, Predicted=99.200202, Expected=81.200000\n",
      "Month=1997, Predicted=87.516542, Expected=127.200000\n",
      "Month=1998, Predicted=100.329338, Expected=110.300000\n",
      "Month=1999, Predicted=99.366505, Expected=96.100000\n",
      "Month=2000, Predicted=95.732827, Expected=109.300000\n",
      "Month=2001, Predicted=105.051425, Expected=117.200000\n",
      "Month=2002, Predicted=115.773853, Expected=107.700000\n",
      "Month=2003, Predicted=111.944528, Expected=86.000000\n",
      "Month=2004, Predicted=93.137981, Expected=109.800000\n",
      "Month=2005, Predicted=100.912255, Expected=104.400000\n",
      "Month=2006, Predicted=103.493409, Expected=120.500000\n",
      "Month=2007, Predicted=115.681279, Expected=135.800000\n",
      "Month=2008, Predicted=132.334355, Expected=106.800000\n",
      "Month=2009, Predicted=113.116157, Expected=120.000000\n",
      "Month=2010, Predicted=116.653757, Expected=106.000000\n",
      "Month=2011, Predicted=109.527294, Expected=96.800000\n",
      "Month=2012, Predicted=101.675072, Expected=98.000000\n",
      "Month=2013, Predicted=100.043612, Expected=91.300000\n",
      "Month=2014, Predicted=95.132290, Expected=95.700000\n",
      "Month=2015, Predicted=96.262302, Expected=93.500000\n",
      "Month=2016, Predicted=95.675331, Expected=97.900000\n",
      "Month=2017, Predicted=98.248167, Expected=111.500000\n",
      "Month=2018, Predicted=107.620675, Expected=127.800000\n",
      "Month=2019, Predicted=123.439457, Expected=102.900000\n",
      "Month=2020, Predicted=108.477869, Expected=109.500000\n",
      "Month=2021, Predicted=109.301393, Expected=127.500000\n",
      "Month=2022, Predicted=120.884501, Expected=106.800000\n",
      "Month=2023, Predicted=110.672369, Expected=112.500000\n",
      "Month=2024, Predicted=112.245170, Expected=93.000000\n",
      "Month=2025, Predicted=98.627089, Expected=99.500000\n",
      "Month=2026, Predicted=99.402359, Expected=86.600000\n",
      "Month=2027, Predicted=91.240632, Expected=95.200000\n",
      "Month=2028, Predicted=94.056147, Expected=83.500000\n",
      "Month=2029, Predicted=87.607376, Expected=91.300000\n",
      "Month=2030, Predicted=90.454336, Expected=79.000000\n",
      "Month=2031, Predicted=83.379502, Expected=60.700000\n",
      "Month=2032, Predicted=67.583390, Expected=71.800000\n",
      "Month=2033, Predicted=70.262830, Expected=57.500000\n",
      "Month=2034, Predicted=61.906940, Expected=49.800000\n",
      "Month=2035, Predicted=54.544915, Expected=81.000000\n",
      "Month=2036, Predicted=66.043718, Expected=61.400000\n",
      "Month=2037, Predicted=60.421200, Expected=50.200000\n",
      "Month=2038, Predicted=54.005854, Expected=51.700000\n",
      "Month=2039, Predicted=53.335252, Expected=63.200000\n",
      "Month=2040, Predicted=60.161453, Expected=82.200000\n",
      "Month=2041, Predicted=76.177850, Expected=61.500000\n",
      "Month=2042, Predicted=65.933616, Expected=88.400000\n",
      "Month=2043, Predicted=76.386904, Expected=80.100000\n",
      "Month=2044, Predicted=77.896201, Expected=63.200000\n",
      "Month=2045, Predicted=67.952774, Expected=80.500000\n",
      "Month=2046, Predicted=74.716556, Expected=88.000000\n",
      "Month=2047, Predicted=85.642824, Expected=76.500000\n",
      "Month=2048, Predicted=80.831699, Expected=76.800000\n",
      "Month=2049, Predicted=79.247157, Expected=64.000000\n",
      "Month=2050, Predicted=69.496637, Expected=61.300000\n",
      "Month=2051, Predicted=64.921358, Expected=41.600000\n",
      "Month=2052, Predicted=48.347530, Expected=45.300000\n",
      "Month=2053, Predicted=46.945968, Expected=43.400000\n",
      "Month=2054, Predicted=45.585662, Expected=42.900000\n",
      "Month=2055, Predicted=44.961588, Expected=46.000000\n",
      "Month=2056, Predicted=46.766411, Expected=57.700000\n",
      "Month=2057, Predicted=54.707259, Expected=42.400000\n",
      "Month=2058, Predicted=46.772520, Expected=39.500000\n",
      "Month=2059, Predicted=42.860568, Expected=23.100000\n",
      "Month=2060, Predicted=29.503720, Expected=25.600000\n",
      "Month=2061, Predicted=27.668588, Expected=59.300000\n",
      "Month=2062, Predicted=42.423029, Expected=30.700000\n",
      "Month=2063, Predicted=31.475016, Expected=23.900000\n",
      "Month=2064, Predicted=26.894122, Expected=23.300000\n",
      "Month=2065, Predicted=25.462401, Expected=27.600000\n",
      "Month=2066, Predicted=27.834107, Expected=26.000000\n",
      "Month=2067, Predicted=28.027258, Expected=21.300000\n",
      "Month=2068, Predicted=24.783580, Expected=40.300000\n",
      "Month=2069, Predicted=33.614560, Expected=39.500000\n",
      "Month=2070, Predicted=39.276611, Expected=36.000000\n",
      "Month=2071, Predicted=38.909510, Expected=55.800000\n",
      "Month=2072, Predicted=48.894590, Expected=33.600000\n",
      "Month=2073, Predicted=37.429190, Expected=40.200000\n",
      "Month=2074, Predicted=39.389308, Expected=47.100000\n",
      "Month=2075, Predicted=45.675787, Expected=25.000000\n",
      "Month=2076, Predicted=30.790271, Expected=20.500000\n",
      "Month=2077, Predicted=24.597283, Expected=18.900000\n",
      "Month=2078, Predicted=21.651852, Expected=11.500000\n",
      "Month=2079, Predicted=15.729057, Expected=11.500000\n",
      "Month=2080, Predicted=13.836235, Expected=5.100000\n",
      "Month=2081, Predicted=8.959186, Expected=9.000000\n",
      "Month=2082, Predicted=9.774086, Expected=11.400000\n",
      "Month=2083, Predicted=12.065002, Expected=28.200000\n",
      "Month=2084, Predicted=22.807370, Expected=39.700000\n",
      "Month=2085, Predicted=37.135545, Expected=13.900000\n",
      "Month=2086, Predicted=20.067392, Expected=9.100000\n",
      "Month=2087, Predicted=13.398339, Expected=19.400000\n",
      "Month=2088, Predicted=17.237274, Expected=7.800000\n",
      "Month=2089, Predicted=11.519906, Expected=8.100000\n",
      "Month=2090, Predicted=10.223666, Expected=4.300000\n",
      "Month=2091, Predicted=7.367030, Expected=21.900000\n",
      "Month=2092, Predicted=15.920562, Expected=18.800000\n",
      "Month=2093, Predicted=19.382522, Expected=12.400000\n",
      "Month=2094, Predicted=16.184764, Expected=12.200000\n",
      "Month=2095, Predicted=14.657431, Expected=1.900000\n",
      "Month=2096, Predicted=6.849697, Expected=16.400000\n",
      "Month=2097, Predicted=12.401344, Expected=13.500000\n",
      "Month=2098, Predicted=14.486521, Expected=20.600000\n",
      "Month=2099, Predicted=19.884139, Expected=5.200000\n",
      "Month=2100, Predicted=10.412477, Expected=15.300000\n",
      "Month=2101, Predicted=13.645145, Expected=16.400000\n",
      "Month=2102, Predicted=16.876438, Expected=23.100000\n",
      "Month=2103, Predicted=22.461955, Expected=8.700000\n",
      "Month=2104, Predicted=13.828262, Expected=12.900000\n",
      "Month=2105, Predicted=13.919713, Expected=18.600000\n",
      "Month=2106, Predicted=17.961979, Expected=38.500000\n",
      "Month=2107, Predicted=31.609092, Expected=21.400000\n",
      "Month=2108, Predicted=24.695750, Expected=30.100000\n",
      "Month=2109, Predicted=28.596797, Expected=44.000000\n",
      "Month=2110, Predicted=39.798351, Expected=43.800000\n",
      "Month=2111, Predicted=44.912389, Expected=29.100000\n",
      "Month=2112, Predicted=34.943552, Expected=43.200000\n",
      "Month=2113, Predicted=39.789730, Expected=51.900000\n",
      "Month=2114, Predicted=49.424943, Expected=93.600000\n",
      "Month=2115, Predicted=75.200261, Expected=76.500000\n",
      "Month=2116, Predicted=74.731727, Expected=99.700000\n",
      "Month=2117, Predicted=91.215618, Expected=82.700000\n",
      "Month=2118, Predicted=85.457736, Expected=95.100000\n",
      "Month=2119, Predicted=91.785680, Expected=70.400000\n",
      "Month=2120, Predicted=75.816972, Expected=58.100000\n",
      "Month=2121, Predicted=64.012713, Expected=138.200000\n",
      "Month=2122, Predicted=78.366517, Expected=125.100000\n",
      "Month=2123, Predicted=73.710097, Expected=97.900000\n",
      "Month=2124, Predicted=67.173548, Expected=122.700000\n",
      "Month=2125, Predicted=100.561027, Expected=166.600000\n",
      "Month=2126, Predicted=176.119623, Expected=137.500000\n",
      "Month=2127, Predicted=145.432363, Expected=138.000000\n",
      "Month=2128, Predicted=141.951259, Expected=101.500000\n",
      "Month=2129, Predicted=109.334617, Expected=134.400000\n",
      "Month=2130, Predicted=118.594707, Expected=149.500000\n",
      "Month=2131, Predicted=142.041898, Expected=159.400000\n",
      "Month=2132, Predicted=159.398981, Expected=142.200000\n",
      "Month=2133, Predicted=148.408755, Expected=188.400000\n",
      "Month=2134, Predicted=161.590411, Expected=186.200000\n",
      "Month=2135, Predicted=168.712208, Expected=183.300000\n",
      "Month=2136, Predicted=176.892703, Expected=176.300000\n",
      "Month=2137, Predicted=178.045649, Expected=159.600000\n",
      "Month=2138, Predicted=165.793217, Expected=155.000000\n",
      "Month=2139, Predicted=159.456448, Expected=126.200000\n",
      "Month=2140, Predicted=133.690146, Expected=164.100000\n",
      "Month=2141, Predicted=144.375096, Expected=179.900000\n",
      "Month=2142, Predicted=170.184646, Expected=157.300000\n",
      "Month=2143, Predicted=161.329252, Expected=136.300000\n",
      "Month=2144, Predicted=143.264647, Expected=135.400000\n",
      "Month=2145, Predicted=138.857420, Expected=155.000000\n",
      "Month=2146, Predicted=147.609321, Expected=164.700000\n",
      "Month=2147, Predicted=161.731956, Expected=147.900000\n",
      "Month=2148, Predicted=152.952082, Expected=174.400000\n",
      "Month=2149, Predicted=163.091860, Expected=114.000000\n",
      "Month=2150, Predicted=121.920654, Expected=141.300000\n",
      "Month=2151, Predicted=127.094634, Expected=135.500000\n",
      "Month=2152, Predicted=129.793767, Expected=156.400000\n",
      "Month=2153, Predicted=149.746861, Expected=127.500000\n",
      "Month=2154, Predicted=133.038394, Expected=90.000000\n",
      "Month=2155, Predicted=97.920654, Expected=143.800000\n",
      "Month=2156, Predicted=109.591452, Expected=158.700000\n",
      "Month=2157, Predicted=129.862836, Expected=167.300000\n",
      "Month=2158, Predicted=153.562631, Expected=162.400000\n",
      "Month=2159, Predicted=161.685509, Expected=137.500000\n",
      "Month=2160, Predicted=143.965599, Expected=150.100000\n",
      "Month=2161, Predicted=147.320158, Expected=111.200000\n",
      "Month=2162, Predicted=118.337012, Expected=163.600000\n",
      "Month=2163, Predicted=128.489952, Expected=153.800000\n",
      "Month=2164, Predicted=129.844708, Expected=122.000000\n",
      "Month=2165, Predicted=119.079846, Expected=82.200000\n",
      "Month=2166, Predicted=89.303574, Expected=110.400000\n",
      "Month=2167, Predicted=96.095476, Expected=106.100000\n",
      "Month=2168, Predicted=100.574430, Expected=107.600000\n",
      "Month=2169, Predicted=107.421592, Expected=118.800000\n",
      "Month=2170, Predicted=116.684399, Expected=94.700000\n",
      "Month=2171, Predicted=100.602925, Expected=98.100000\n",
      "Month=2172, Predicted=99.353131, Expected=127.000000\n",
      "Month=2173, Predicted=113.596847, Expected=84.300000\n",
      "Month=2174, Predicted=89.567754, Expected=51.000000\n",
      "Month=2175, Predicted=58.717041, Expected=66.500000\n",
      "Month=2176, Predicted=62.152766, Expected=80.700000\n",
      "Month=2177, Predicted=75.544301, Expected=99.200000\n",
      "Month=2178, Predicted=94.977504, Expected=91.100000\n",
      "Month=2179, Predicted=94.622655, Expected=82.200000\n",
      "Month=2180, Predicted=87.359000, Expected=71.800000\n",
      "Month=2181, Predicted=77.510610, Expected=50.300000\n",
      "Month=2182, Predicted=57.661132, Expected=55.800000\n",
      "Month=2183, Predicted=57.090316, Expected=33.300000\n",
      "Month=2184, Predicted=39.652449, Expected=33.400000\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(test_scaled)):\n",
    "\t# make one-step forecast\n",
    "\tX, y = test_scaled[i, 0:-1], test_scaled[i, -1]\n",
    "\tyhat = forecast_lstm(lstm_model, 1, X)\n",
    "\t# invert scaling\n",
    "\tyhat = invert_scale(scaler, X, yhat)\n",
    "\t# invert differencing\n",
    "\tyhat = inverse_difference(raw_values, yhat, len(test_scaled)+1-i)\n",
    "\t# store forecast\n",
    "\tpredictions.append(yhat)\n",
    "\texpected = raw_values[len(train) + i + 1]\n",
    "\tprint('Month=%d, Predicted=%f, Expected=%f' % (i+1, yhat, expected))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test RMSE: 16.803\n"
     ]
    }
   ],
   "source": [
    "# report performance\n",
    "rmse = sqrt(mean_squared_error(raw_values[-2184:], predictions))\n",
    "print('Test RMSE: %.3f' % rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vD2O6+WPsQ9cUqwapjILjaZpj+2audqVBZdl5wNZK3+sBsDzIn113\nBJahV/A5EWGQAqsXOQgzxS5A/u87PggvmMMQJb+MsmMbroyNzX6PxxMO7fvOt/0H7KBCN1GpzpjP\n6PWNl1n2yYp3io6VW3RzjJfnWAiNXgLzPh+m2aU/rUdjxu8dNPel+h9rbcOzqIk7lvuRca7z8b9+\nLgpgVISgbwLGzlqLc5/51lfQt97gnvhJcjHd2DlO/gHLZk323D9uprtZwMv7Y8vsz3yvp51s/Vue\nUM8MPsdGUNrmlEKoqt6B16evxKxVIZOThXA1ZSEiEYl7FVezLo79flHOuRCl8LTdBKhQzOFGmgiI\n4By/IMyMJPzfuImZM8T/qkfgrvT52e/L1nhf609vaIXBvQR6mDoMFPCOGAup58fGofVCZzEZA0U3\n61zXeDlYqwpbP9ziMXx+Y4tG71QsVC575c6pQ2xFCPom4JrXf8T0yi2+Nvo2G90LD8eghkpxcPPb\n32PVlnrXfV6ZJh/NnOW6/V+fzcW0Zf7BVJJt0HJLebxgfTU+mLXW06Xt9W+X4KH4U57XKKcUDpIW\n4JZ3Z+L0J7/27Q8A7GhUsL0u2EtKzQRr9APJdNF8KXOcY3/lZvffOleGSktwmvQNVm8N065VMKhc\n5LRBHJkmESBZHKl4ze+dqAaP/+cV99P0v4W8FlNDDNxaG36LsWYbyQ3edRQMEwoDOeozK5JLAsCM\n90zFotF36ue8FtffXAIpoyIEfRPSevH73jt9AqbUEIKeAdjsEcjjVY7vFeU4PJM51bH99vgYLNrg\nHwFo98xw6/4Jj07G1a//iCfGL3FtgzbOw1myt4lhqKTNRE6XgoU8AJzz72/w+LhFgcepmWCN/tbY\nSwC05FbPKic79vNRxoXgKHkWHks8gRH3TQg8Vralbq5uBDba3BPfT94KVu3tTCCrhV1TGZqyKir8\nYuPeUiWurrwS2OKs8GQIRCblbroJ1Oi5hVS/oU/VNe8/HjXIkXhMdXOvTHsrFZa1peGXOPYr/MAk\n3CtzJMSLXAx+muWdFsBN+2KMIeayGOt6PsjTnOBfd9V5zlR1j0CzCtlMBW79/y6pefZ4xSKoblqS\nCzfHX3Ptp505a6pDuSqyEO6VRg6ZrWiLh87dz7H/mth7gW3sLGTbDK2RSXhaOQ3VrJX1wKqFnm3k\nkhXUzlqf2YdrcJOLm2GwZ0+wiJJYkEZvCum0n3el/lx0bNfauc+tm4rfYMmd4JafivGfxWJsZKpn\nfwLcVQHM+W+xu+JgUmYvz33ugj6cjR7QBL3XVN3PL9rtRZuv7hqYlMyebIwBOKjhCcu2CjKiS91f\nwhhnR7anUbC30w7hTCVSiEIlYUw3htasMgnH7ukMBitYdGsOyDZ7fgYyurZvjYmqteyiVzFtoDCC\n/vnJ7rOnqTcfg/atXAZx2RlUlX3+PJQZv7+BO8r3HeFNN63nv+3djK4gkksWTVclykcTNzT60Rnn\nbBAAVO7vEgFTOfDWWM0bQV2cX4GJnYH/ApmLZr1ss5bULES+eU2jd9/nlwHS7TVKIh242GgfPM4/\naFdsgIsPtQ/fLjLt4JmATJphBGsCaQyg4GIeaojFWGNxMx6XXTOGtkYDZoZdIC4wdkG/O62GRIQG\nZhWkvuaMEII+8Bf3mDnv0r4MHVwiZRWXxUtj5uS16LqDU8EdMxa+DZ8BgU+n0xZ1nscZGr0UC5mQ\nP2Cm3MDi+GfmfNe9qsp1aifUOLDT4gR9Zb2mScyr2vmJgqLSt6P3A+QmV897bhpkUqCGyE7JQJ6F\nTbbUuD/cN5wwyHV7koIFvd1F8Y7T9nY9rBdVWTR3no1bzXwyrmH8HGHyrt8Tfw5jEvcFHsdCaPSG\nF0zvig6uNQDOi43HGSEWiHcGsk0wlFMjiFySfvlpuQXQIof2dBe8XshPHQg0WmdmFCDopy/dwH1z\nfyYJqq+/veRRb9mBLugp5hyk7HmYAFhSJjj6ZK8i5Tw5+0n40eeAYaONhR2Vm5ABnfz65J2P/qe1\nwalRH4s/DqnBXcP890T3KfYVR+7marpJIh2Yz4X0l6IeWn4Rr5dpSvJanLbmYdd9vO94UKHy3Tgv\nGC8OleYGHgMASoCgX7m5PltgglE86xGywTMfSzg8c9xzvJe4FdUN/v2za/QAsFePdg4N3G9th0Kk\nOQiyn/MuodWS9bfx1BOqrfcx22ePQekUaWr2c8zLMQfM18TDz8i+U3f3PI7pyovsIugPHeB0sT3m\nofF4wqNkJgWkZZA5jx1ho8+B7m01E0AyXkqCnmFvWobBK17zPsRjVJehYs+ewSaRXaUq9PzpMcf2\nVEbxDcbxEvR+Gn1jRsWyDdqgclU76zXHKs5cJ7tUfevq+jmsl7no1b2Te6SugVvqADv+OdFNZq/c\n5Lv/j6M/x16SVrCbSTEQAfs3PIOjUu4DVlh+/x/vItkG+0lL8NQjd/oe4yboH/n1UMe99DPdJKPX\nqnFgjUewPy9ebmTWC5uL+u5C8b7MSPNUj1mdZv7x0ei5prcz50KrQU2t5klFsXBOAhIYHvzcXYki\npvqaG6vLemQ/BxVEKQQtTtDHmDYqh3FJ9GPVlnrIUHCx/GnefTpfHocPk7egv+Tt7qbCfUFWhooO\nbZwJnz7Qa8nySGmnMB10y6eI2V6Q66Ubsp/dbfSNvvVtX5m6Ijt4bI1ZA0vcKh71lqpw4xjnmknn\ncvMexQswMPsVqOZ57/tKLFjvnoYYAC5reC77mclxEAFb0C7P0ovAsOVPhzruptS/fPdLLoK+VSIG\nyV77z890UwC7ML+o7fDC8jJH2NwUjTvmpZHPZ7uap3oIemJqgI2eW/j0EXkTZ2nuvOXtwq01GdaD\nNds8/OmJMPEvR7ruapTKMLjhRa2d6tWhrpcPLUrQpzKKKejz/NMOv38CzpEn4bb4S3n363Q52Jb7\n7ver8PsxMxzbZSiuxb//nL4CI2wCwbscoc1Lg+Ke+wDNRq/4aPQNGSVbUo1fKB51yp6OF96gbWaL\nY5slp4qLp0NUwmr0MSio3uGtRSU4s4ZKMe9gnoicI08qSDt2G/3nyjAAztmZYboZN3+DI+UB7+kx\nUbF665gNBORP4jT65zteZ9nn6ellG3wM4e0aeartwZOZ0zBT7Y8E0nh6wkKXALygFAjm/WvXyn2w\nZozh0YQWvJds09mzLZ6DJC1r7GH3jnfptQqQhL5d3GcQjAENSKKRyZixtLDJE93ISxoSUSURzSai\nmUQ0Q9/WiYi+IKLF+r8dC9NVH5QMvlq0ESNHPQ65vgpAYcKKe1GV5XttKoOUT66MqLyrjMh+7krb\nsH6hMx+NDNW1JmwaMaxmFY7tdo6TZuBceaJ1I6fhlMPpOXGQtADk6yOsuUammWwpyDCsT0fPGqaN\ncApyi504Yi4RN8IO7lpOee/nQ+FspvXt+men/qE8/QKuGxq/qky2duaxPgCAStXmBkoypi3bjEvG\nzMD9n1rrEfCxBAzATLU/AOCaxqvM0wNs9EYblzX+CQs6HGm9tNeMwWaPNn5Sv1QHD2RG4n/6uzL6\nsx/w+nSzWIqqskheN13aueesTyvc3+qR8G+bzeyTLWHogma68X4ejaupkLBxe2GjrN0ohEZ/FGNs\nKGNsuP79JgDjGGMDAYzTv+9c7uyMw18biPeS/8AFMc1EEFjxPQRXxayRrHv/4zOc+dQ3kdrY0ah4\n2urSzBRuF8S+xEdJZ/k9rxQI9581BHedsTcObXDa5XmeTTyM/4tZc+rzvSknd4F+7JJ/+rYbg4IM\nZMjcCzZ4l7aegt5N0yc+mdNO1uiXc0IwjozvGgQv4JYP/J1FCF3UeGPO/YsH5J+x4CfobUKU6Sar\nJ5Uz8PvG683tALbWawP5KltwEx92r0LK3rdK1g2LVK26UmAwk+5emYGcLepuIOn3NsNs98Qm6O+M\nv6B98NDI25Vp70iN7lrZlnagIW32XTGCCn2eH/4Z9VoLy/DbZfe2jtTXaH5gAz2vZUABiqbx/KmQ\nINtNbjuBnWG6OR2AMdSNAXDGTrhGlg2bt7pu37XyrZ1yvblrvW27brzxnUspO51YiHSwkoegP/eA\n3vi/g/tgLZzeAEGcOsRcCJquDnY9plutdzETAiGBDNKI4fCB5qyiLC57CjO3dMNWQb9zNXreTz9I\no7cMy3IMEgG7tCvDfWcOwdeqFvRmCMMoRCow4uOJYdfoTx2q3c+YHMN41YziZUz1Hi+4374sEcdW\nPZOpZeYV4A1ipAxII4aLD7Pmc5F1E2qKbAubtjZPlvUFag+NPKbPGOuhtbM3Lbf8jorKkEAGqo+g\nJyK8mDkeAFDXkMKVr/3gMP8YGv1a5m2f34a2GNjwEp5hZ5tte95T5lvL2bgvCiTEm4GgZwC+JKLv\niehSfVs3xpgRtbIeQOFrzHFs+ck902I5K1wJwHxQVOa5iPSjulvA2QxxUkIW/w7PiIHm4PCKcqzr\nMV12LMfKe4a77gM0YZmGjKuPtv4N7ch9GuqmHUq8L/6wi316HA5/QW/uiwcKenOfJMkgIkz92zE4\n94DeyCCGNawzZgbeOyfRTDfeQta+kNpKL7rRpixm+Q1mrtya/Uvs6wy8Rt+3oh3+lL4Co9IXYwHr\nnd0eqNHrNvrRFx2Mob2t7pVlTHsOqsmaCttrkdZrHeT1PxyMa47eDfsN0AazpxKPYdjyf5t/B2OI\nkb9GLxFwe+YizFb7oqq6Hh/9tM6hsGUUFSkWw/vKYZ7tANqg1rmNaf7xDIIMMN2ctI9WaEUFoVVi\n50dZ5ytBRjDGhgI4EcCVRHQEv5NphnLXp4WILiWiGUQ0o6qqyu2QYBqqscekP7ruqmX5eUi4E33k\nVRnDAZK7C9abylEY2XiL57nGdJqFiIwNg2FjtCpP3g/ZrikPH2E1gwtiX6Iz1Tj8570yYq7d6gza\nstjo9/21Y/8Ctbdjmx+Kz9+yA6ZmGUWjH7Gbc8bEQFkPl8Ubanw9lHgKJejjtpmgTEZhDSt3fWjm\nzHcozNwajEoytqIdXlZ+iXvPHGKeEzQD0d0CpbjT7/yd2Kn4QhmGj5InWrZ7mVS9rjVol7b48y8H\noUcXU9Puuv0nswsq0zJ1+plu9GdUgYQR0hx0xVYotgFn0brtSFIGvbp4LymeM6wX4jLhgAHmLPY0\n+RtMSV7jTFkcMBvq16U1pv/9GKiQMKhrtMCzXMhL0DPG1uj/bgTwHoADAWwgou4AoP/rmoyaMTaa\nMTacMTa8oiJ4UdGNWQu9y68tZoUvhPFK/J+RSr4BQHKHdRA7JXVX9nMaMcxWnSlMDYwpqp+mOngX\nTmMKUsD0drw9HMLRuc49GyUATFH3wT3p3zi2nyV/5dgWFIZ/VuNt+Hv6d6H75Wej38E4QU8ZX68i\nXpO1p6sFNJu4IZiOe2Qynpzg/XtkqduMWIg8POZFvI+1t2NEcp4yxF6Oz/tv3PurK8yjuMX+kQea\n7oxBdmam2+jdAozWojP+kL4eGcmqcHnldaGA4huU4BZRuedXVTWtmvmY/oxxuBttQxmlcX98tCMg\n8IY3tWLwsTJvofvAOfti8d0ngcXNYx6Ij0Yv2oSGGmtab4lloAQoaHFJgpJDFbVcyPmNJ6LWRNq8\njIhaA/glgDkAxgK4SD/sIgA+uXnzo08b74ejHCnfEOVcGCHPxdjkqEjnSFx1nS+UYZjDNO+GNdAG\nN/fCzhqGLdYvJuDNS80ApSC90rC/ho0I9yIoydpP+t/I41beL+jlrkM5VoXwLDLgB8RnMqdY9vG/\nTRyKrxbu5nJq8NLvDkRvqUpPr6y1ESbnTWb0UYHHWIhgujEE/a2n7oVPrj08u70neQeGdWRmn5nt\nGTQUjKD7vGS9tj4muQh6Rbd5L91uc/n0eCcl5h8NLCVM4covjissWKM3Flq7k+biO0Ra6pjRyYpm\n6nXNO2+jtnVfx7YXxs+29pdlAnNUSUSao0YpC3potvcpRDQLwHQAHzHGPgVwL4DjiGgxgGP17zuF\nsg67eO4bLK1C5p3f76xLh4bPU5OBhH/+ah8c2vAYzsED+n7vW5DV6P1C2bnTg1xKDXdOqSLYa8CX\ngIEiiXCl+gwb/VGphzyPCesbbz+20ZYkbYRspkeIQfHV6MtcXE4Njtidm7ZL4T2wYttXhD4WgO/L\nb58JSbqXiCwRurQxBdXoxCMoq12NODK+WuO67segWzvzPMPuHOSuulQX9G5eKsbvO0/ta9muegn6\nADORlDQFPR9cpai6141LZkyDijZJXHyo2Y8OqHN4XfVpr/2tHds5y2va+X6j89k5bRHnXMgYjmqc\nhK6Ztb7tkARdoy/hpGaMsWWMsX31//ZijN2tb9/MGDuGMTaQMXYsY8wZKVMgEh39zTOxecVPVczn\nsVAg4aR9dsFadEEdtUbPDuW+ybwMzdI3Z4nPte1BMlWDzsPuDWNAHftmtw3epS2GNDyLxzJRnKP8\nJf08tU+oVoygmkrmvl5//9lDoIRI6GbAC6a1tvJ/KWYKoyAbfRmFG6geSzwJgpq3f70rfoLeNhOi\nuGnWiMvWziTr12Fx2YU4a7N7VO4fG6/Dup7H4YOrRuC1PxwEAEiQEV0uYdKiKs9aCdlcNy5C1jCN\ndGhrSz/t8XdJAUpKzNN0oyAesBhLRLjtNDNFuETMMQs7ZU8tSGpov2Dfkblrt+MLPUjNoFeDuZ41\nc1lwXiatH6QpJ6KUoD+SRL7aYD4UrIIQ91KmEUNZXBNcZ+7fE+9dcSj+cap71kfA1Oj9tFo+vNv+\nuKy1hWbfdsb+WHSvVaA//pv9UI3Wob1IMoqK56cs99z/vysPw0Z0xHWNlwe2RWoGCiNP74Rzh/dG\n707eeertKJzP9szOp+LaRtMOvZ6Zi2y/jX2GDpu9i8D4afR2rpL/F/rYSHgIRMYY9l36b+vGDuai\ndUy2/pbfLtayPx6xfSzcMBaIu7YryybuMjT6RoVw0QvT8fr0VY7zjEVQAK6uscZi58hDBli2q5z2\nuoWriBa08BuPmzMO4p6XTFpvI2IcxgOfLcS4+WZmTMMxwC1zpZ3ObZJ4WznCc/93y8I5l0ikp98u\nZY2+VFjO7AtQhWFUzL3GZWS4xad9+vZAWVzG7Nt+iVtO3hNd25VZTAGAVQuPZW2lPho9n9aaAYs2\n1KCqRvOocJgn2jq1FWPgGa/uj8Ma/oUPlYNs/be+gJvrGn39wQ03O9cgMftCnJr2XaMAgA7knT/c\nDt9WPB7DR6qZD+iC9M24NX1R9nuf5d5xFuUIn+L6EGle8EG54KHlZVSGvpIpoB5Inwuljyl0YrYF\nmB9W+k+oy9DocG18KHMOAFPBsAdbAXqgEnlr9A+fOxT79GyP9jaNnnFunQvWbc9+DsyUmeBs59zf\nWCHEl4UAACAASURBVF2rPR+JZLhEZDzLqsxni3QzInkES/Ec3K+Ta6R3tnshMoMCukbPJN96EYWi\n2Qv641yq/1ioCq4h6oZXxGhU+Gl2opVm/2tbFs+6fNlDv7fvMM0Gu0uaJuWXrIvX6BsyCp577HY8\n9fA/AMBinvBLz2qwBhX4zh5AZUuFIEuEffVarjM82px68zHuKVqrrGH4pGbQiDjuPXMfzz4ZOXXC\nwJtuTth7F8tgs5J1w0vK8dnvkuptnkmGNN0AmhngzC3PA/UFtlB6avTW7y8rxyIe42IEbBr9awn3\nCGejxuy36p6Ofa8ox+Gh9NnoSLVagjuP6mcj5QnaFxfheNTgrvjg6hEOjxyLKTNtPltBNvpYjJ81\nmPe1tl5bRE0ko7lTt0etdb0ggqC/9tjdsV9/p9x5f6ZmspECnAwMiIzBtLQXY0uCZy/0DurRyM3+\nFaRphoYb3Tf1O82x2+EBw71Ud8e08PAO1T5Rqtz5A1e/h/vjz+IfTLPHZrj8HV4La+3KrQ/2GOWX\nGJW+2Nxgq/PJGHBP/HkAwI/MXdDv0r4MfTo7kzk9NrHSYhuV1UZAjltc+uyQS54fL/jB5YojB+DR\nkfv7HOz9Mnom+XLhYGk+Ttr+OpQvbwt9jp1q5sy/8tiXCy2h/gZ2oVuLVlmlAdAGYrdU0XZXyblq\nH8xS+2MtuljON1gHzWbdlba6Ti4UlWE/SXcr9RGOdo8cxvs1pjnTYoCHD3H1JXj3YKPQe9jUwgaz\nyi5Fr3GmeZF0P3jyWdQ1kCVCj07tHduvfWMmAODtaeFcsCUizGN9sb2s8K7gjmvt9Cs0AVc2XuO5\nj2Vyi5ANKm0XllWbTVv/ji5OzdX+klGdOS03ps7xRu+0C36ZFfn8He3K3F/G9uVxfH/LsdhXN7kk\nYzJeVn6JzxR9ALUV0uYX5nYb4R4cBQCq5HxhPp65MluVKaOo2FZTh0yAC1plxZGoZ+FeYn4tg4jQ\nubX3eeSj0dfCPfGVH6u3eKSqdWF8p5GW726D8MtTKzHmm0rHdl7Q79/wDFRIDi3+HR/7sYEMFRnI\nuOiQPjhhb6f3Wp0ecHh97G1XV1SLWTDmrU3bBTDvR6/y1aYC0opbBDAn6I0MmmE0cTsny9OBHbri\nYWj0IQsWuXn5XCJ/BACobwgncyQiXJW+Bt/2CV7PypcWIei/Ur2n/pnG3EwwYXObB/HDMjNezM07\nozwuW3y+48snZD931otrS6r338CPE1XMqmVkuBfUrYZn9jptkuiml0ob87sDkYhJZs4Um+mGf+c7\n73W0Z5szyp1a5afJm/Bs/EEAwENfLEIMGTQo/i+4LMcwWtELLAcF8DhK6Wnf18vdMayPNeLRz4ff\nWKA8JvWA7/V4+lS+BSwJV6e41f7nYkjD6Ox3YyYySzXjD9pRvSN6E9B+f6PS1RZoWRbtdnm3gcNu\nAy+TVXRsU47bT9/bMVAApnvqGfI3roLeYlnyEfRwLG6aJ6qNXJWlgJmbLJv7efdKI2grjCb+dOZU\n50Z9xiplTTfB7QDuisyo+KsArJW3/DBuW2DZzgLQIgS9n5lFSeXmPbMR3mXj+t70IZ6ZFG56Vkam\nZ4HsIunL4jIezJyb/W6E8SuKml2IXNTHGWlqwNv4U7YFIosLYcDU+IGz98W9Z+6Dg/t3xjnDeiFt\nlPazFdLmH0q3Kb95Ofd7cpysebvMWbUVZ8lfObMbuqDqxzQ2+nvD2AU9A3BB4024rcvDeOPSg7Hg\nzhOy+/xs9DJUbGetsJRFS1yWmRFcu+DlzLGo77I3qmEuUhozkR9UM75hXPKv2Hf1647zFZVhM2uf\nzUEPOO+Du9iwbo2xjK8WbE1u5hwULRq9j3+pbNOQebs4s5hugoKLzM+b68z+RNHo78v8xpm0TB/w\njYGfQqbLVny8fDzz39gw3l27G/TOoEUI+mH9nPlIftf4FwAA2xwtZYHBep8sdqdJ32DxV++Eaod3\n1Rve19lmWVy2DFTGS//t4nXZbRs6eq9D8C+AfUErwz1ArRr9Xb7atzJt5TecMDj7orOMXaNnWM26\n4H3lUOzVw2mnNIhJ/o/WofVasYbetMH3OMaANbpP/G/u8y7FqKgsK+jTZGpbX6lDUB3rhLgsZT2M\nAH/TjQzV16X1iczprtt31AXX9q1BK8sCOmBq4PZr9ts0AXaYHgnaiBguGdEP0/52jGNBv2cHZxi/\nXRRLPql9bzt1T0vcgdvsxy8OwXIdW98Y3xYv6AOeF76d5ZtNk49R6D2MWyRgTYUBIDtjNf5GKaRG\nz3wiaGO6oL8l/dtQbb3wtbe7cqFoEYL+siPNRcFXMsfgb7gKU3RzzvyllZHbm7t2O34pOas9GTyW\neBIPZfzztRvwgt5NA5Ylwpn7m4sxmYQmPDMZ87yT9/XWLPmXvAdZPT9Uzr6uRqhL2b48jgHdNVNH\n1k9ZhzFtQOEFgRuHD/RPn9yKhXObJDJnVx0aViGVUVwDeNKKiv6kRSJO6qFFRBvCIRlzPuaxjHex\nh7YJ+AZq8TMwnoyHuY/vbxoxx3Pwnh6xbJjqsrjMilSm5bVPI4ZRp+yJbu2cZpM9XQdgm0YPxTNE\n/+LD+uHiI8x3qmu903PNmNktVf3dm2WJ8HjmDDyYPkc/0VQ+Fq42zZq1/U60n2rBGi9ifq7apv1m\nYQW9PWLayKlv2ujDafSqzwxiV9L+rkrmHblvcM0xAzHqFKfnU6FpEYKefyFuyVyCj+gXWY203eqJ\nkZt75IvFOEKeHXhc3Rb/EOffvjgd/Wmd7zEA8LvD+uHk1N0AAFUXrAonYNuVR/cRBgBFf4g3sA4Y\n1erWSOfu3qOL3g+n101cLzrix1nDzMHrkIbHHfsb0uGmq38/eY+sK+DziYcw6JZP8fJUZzoBRWXY\nXdLc26b1uAAAcFC/TrjqqN1w/9lOL5qK2gWObQZtEgSVJHx49QiPI9wFuleUMz8uNbIY2ts8ne7L\njMQ+Dc9hCC2znudiblNUhjhlsM+uPjmAQgTgxJh/IjCKmwPIHxdf5tivMoYtrA2+Vr0D/gBtxvlQ\n5lx8o+fxf/9Hsz7q1EXm+5Np55+plB8cT5O/NdufppX/S9T5v4sA8P0tx8Jx7xS7jT7cu+aXcuHx\nxBMArIWFvPjzcbvj/IPCRZLnQ4sQ9PZsjAMqTNe+3RrmRE5ulkqH035nPeZtOweACQur8Jf424Ht\n1KYy2YFJ1b2EGFd4OSjG/t+Zk123K2mtjdGZkxHvNiiwHzyG94GStnoQzFm7HTEoGNa/q+/5vAa2\nDp1Nm7/O8pQWU/BG5kjfdrq2LbOlM2D4cJZz8OQXno3oUEki/OX4QahoG22glJgCWY5j757epqlN\nzFluzsvcw8+salCOPp1bYwJXNJpBQg1auSyiOu87Y0zP1ugzowrw41ar1+uJwLwFkeS3wAptwAky\ncQGmCc/Qwics2JA1+wyu0P6GX6dGBaaRcEyG9Rlqa+jJyBLe98qgc5ukc8HeWMw1vIFCeu8wl8VY\nO+kAT6KmpEUIehDwZOY0jOr8MF763YF4/qIDrClbq7z90HnWbtuBrxZXIaGawu2Pjdd5Hl+u+i/0\nJkOG0ndvX5adUm6r0dpUlfBh+PdkznfdbrQxuEcn/OPUiNNDXbP534zleJOrknXFqz8gBgUxlxzk\nPPYX82XlONfj/qOc4Lqdh9eUtfqgzmNqU6Zwu/zIAc4DIkBM9U0kBwCn6jMwHnsWSIPJE8zMncde\ncBPal8fRjysa3bezZlO3r7G4RUQbphvf3C4ukZZGbYPaDcsgPTwIA6R1vnUOpLj/4KiqmifPgf39\nTXR7dG+LK44cgHMO0LTWMYn7MP25P6EulcGaKi0ydhPca7Ra+mN7oBpqtYRqk1Utf/72Hv4FQwzs\nRj+ma/QT5+szjZCVzvwWYw0uPCx6cZqdRYsQ9ATCA5mRWJjYE0fsXoGOrRN49NdDs/szrzqLWrhx\n8mNf4YLnpyOpmvbjSeoQLFTdAxrawN93+t3EP0Jdt0/n1mjUbd6vfL0EaUWFms4/MteYFRyxRw9f\n90o3DJvnsjnTcON/rWYsP/tu9nxORbvqqN0cIeOGW9zhg4JTWJyxvxlQ1Rb1jjS9AHD50x9lP3vF\nDPCsZt4CSmKKb4re+88agnXojK8Uq9nCa3D4nst90qWdM3fP2KtHYPJfj8JMZhMMbqabEGl5/TT6\nD7/6LvvZV6MPEvRM0+gT8eDn4IYTBqNre3OB+JC1/8GKzfXZLKeNiKFt0r8du8faI19opjdj4bOR\nhdOe7Rq9YZrMesqE9ccPIehPH56fwlFIWoSgzw72fAyHLGV9lVdQuMizrfXag7dbO87XFxK2QjMz\nzLdVPBoorcHEqd/BjU/nrMdeUvjUtBeM0FzrEkhrHiRK+DB8L9Q8gkmMQJdR8VcdCadiUAI1HyLN\n8+k09jD+cvwgpG3abscy7ab99gj36FqeCw4z3Q5nlV2KK7Y/7DjmxnrnNjcOTz2C2WpfJCS/wiMK\nVJ+AuXMP6I2XLznQYWrxij6eudI7LzygDUy7dm6FW/mIZMBV0Kt6MjG/xUBSvWeDjVy0tN9gkYr7\na9mKLuiDAp2yfbJ51cgSZVNNpFgCXV0WlXns3jtV27XF9PZJbfvAbt7u0Dz21ByKHmczkFajjiWB\n1v4mSQO7p5PrMRGjdXcmLULQ9+qkaQtH72G9SdVog3lqH6yrDRfA0IuqcEPsDXSRTY+MNGRc3Xg1\n/pG+CCc23uc4Z//PndGhMyq34NvXrV45Z6Tu8L328AHaCv2l8kdQVTWr8YZlrktq4B+XawJGyknQ\nmzOAXcAXYGd6Wlh/Qc+YlihtObRB1v6CbdFNVD06Bef/5oNlAOCIHePw0OcLLdvakDa7qnKxnfOs\nYt0wW+2PBKmeAVgSC67Te/jACsff5HUOH0CTiHkLiDqU47CGf2W/u80qmMqQIMVXo4wr3pGZGT4F\ngU+QUiOSeDvjHWHLUnUoo7Tr7MoN+zqaLGlKDQB88CfvwLtsVyVgvGLO0tN6crRe7bTfobwsXK6b\nOfb8+OkGvPfjavSkTVjBdgFC+tE3Kqp7GVD+mUoGP9tNRYsQ9D07lOPHUcfhj0dYKxuNvmAYUohD\nbdyB9duDw5IfjT+JK2Jjse6n8dltDBKq0AFjuIRYPO3U7Y5t22obcHt8TPb7j+puzmm5DVn3cugt\nVQFLx0XS6Du3TuDa9JWWbYwxtJ2v+Z3zHhRh4afu35Zdnf2c9QwJmrqaVakBOEsJmlPlMLlFnNse\nH28t35fWNfAlHmY267EyOqhbgds7YMPLLsVpVMU3Y6gXXuaes+VJ2c+7dTVf/kMaHsewBmue+DQ/\nk3DT6DPagKbK3vc0pno/6wqnQNRlvAedVEbBKmYqTmlF1UyK+kJqeuL9AIBeq0IWkLP9LRJRNvNn\nN5e8MXYkIvwufQMeSWuK1Yxlm7C9Po2Vm/T3L6Rt/bbMxZbvSjqF696chSTSjoBDP9IZFVPVPXFy\n6p+W5H7rttWZEeptws0OmoIWIegBoGPrhGM69cu9dkEKcSQpbVms88IIE+eDeF68+IBI/Vi3fQee\n+9xqzomFiJTjCyyzdCqbrCkM3486DktsUZzVOzK4IjZWbzu6oJft005dUzFKKdJm98LhBsZMvWcH\nLW9ML1tZu2yh7BCzDfu03YAP2jEWMsMs7PWj9dnP3ZZavaKWVdUinU5j645gTXUXW9yC4mHuOUWe\n5rp9HTpjM0whd/mRA6xuqy6DzfpN2uyqvLW3tjin/EAAwMkpl1gPLu3Aik3ezgRE1qQJ8Ts7YuJt\nx+Di/2jP9pwFmm99JqRwtJtuiAjHy3qsSgiXxrZl2m+7Vk+21pbq8f6sNfhT7F3tgICAKwP7WpHh\n5ZagDNq3dSbi8+K3I7Raz3NZX0tw5WX3P48Kcip/xabFCHovUiyOJNKhqgAZC6LnxcyIxKMGd8WJ\netKn96441PW8yk3m4u0To/+NN6ovtOyPhch9EeOmjIzBDOQIDVlyyR94x4fZz1IiB43eHoBii5Ad\nuOFj3/PblsXxxHn74aXfaULHHnp+ljxZ+xBC0LsFmlWWnYcfxvw1+326nl658sDbfdu64/S9MJNZ\nF8nSioonxi/G9W/Nwvy11ThanokBFOyXbc/LP2/ZCmyszi2JHgDceMJgPHORmUOfuQiv1A4t+jbZ\nyrsgy4ZYD/RteA1zWV/nzowp6GWfvOm/2q+nY+HyOPkH1C2egh2NCtrqprLGAFu+gd10Y4msDWEu\naVsWx9Pn759Vxj5P3ojOcvhEcgbPXjgc3yimBxrTF2MPluYj4ZNTyk6bZAxf3aDVAa7hso9mM3qW\nGC1e0A+XFmKotBSJqjmBx0rk7m//xHn7Y8GdJ6B7e/eshu/PXJtNKdu3bpZjf6sQhSx4YaYCUH1C\n9N3o36U1arkH7o7Yf7KfpRwWhbbDpt2krZGk65LOAuB2ThnSI7vIdhtX9AOqin2kSu1zCNONl0a/\nz0qzOIwMFXUsiaGD/T0dLjykL1baShdu35HGg58vwn9/WA1ktEG7VYh6BJLNWe9UeSqeDpkDyQuZ\nd1t1c69MafeBL5Ztx68erswJM79iH3FZwncVZzq2/zd5O/a49VO01j3O0rFwWrDd337SQv/UF26c\nuE93dG9n/j5d10/yOdqd4/bshivT1+DOtOaSTNWr0VcPauy1wzuIzo3enVqh8t6TES83B93b4sH5\njopBixf0rfUXtnyt+/SZx8tdUpYIZXHZGbShM238u7j/U31x0EUofaXug5tOHOzYzsPX+hy/YCPe\n+y5a/ouPrz3cInh+HZuY/SwloqfdbWQx7N3wXPY7a9QE4ALd8+jFfuEzOwLADnCDDZ8RM2QJODd3\nSF5QdW8jI40YDnDJJ2Sn0RaxqKoM/yd/gfGJP2N7jXdqBL/rZ7eFLDrh2SafBMymBacVFZXrNROY\nnPQW9EbKhXOG9cJHyoHZ7au31qN3Wy6Xe8BvXy+3w4sZ59rUFfL7OFzWFCeFwt2/lG1Sm/4sWqS2\ngcz95paF5QhsRTu8rhwDAGg343FMTF4PwDnrDAslwpt8ikWLF/Qm/g/Fis11ge6QXi5Ve9BKfDrH\niNZ0HrNnj/a47Bf+miav0X/w07pQ5h6esriMmZJ7UJQcjy7oMypDLUxhsuijRwEAX6t7o4aVI9HR\nP2TdThUz3d/Yam4NI4RtlTHgL2lnGD4//W8dU8GkuCVxmRf29A1Kqg53xV9Ef2k9nvrMu5asHTdB\n/9eZJ6Dxtf/Lfp9RuQXbmCYIKmPWWdB5B+2KFy62JqyTOOE7b12tJU/O3R/Nx8ffazMGKeltujF+\nlxP32QXVzBRCI+6bAOIC8Ybt5R8tLUnkWj/3hvib2c9b2oQLCtqa6I43uSjoy2Ifeh/s1yfu9VJz\nLMHXv6I16uGc5Y4KmYTMTqPkPeiWCj8bQR/fshgYcyrgkrb4+SnL8YsHJga2IUvkyPkOaMmo5OoV\nqN7R6FortXvbYBskn+3xKGmmY6EvDB9IR+LZzEmO7Xb3xDAYf8V2pj3ERo1VGQoUSLjq6GhRf/sO\nOyzbt6rqFCrVbnhPCRvNyDDPxX2UF7MSyyATUrvct681T0xizhvZz1OSfwrVBuA++JSzeiQWfZBd\n0zjvmclQQVipVuDWjlb33H/+ah8cPdhqRuKViROUCVi2wazINX35lmyJy5iPRm+kg5CIMDu2V3b7\nWdLkbFpfAGgVUGdVJuALdZjvMVN3u953v8GODHBj5lKsYZ1DHe+FROZdV5TcBP17lx+Gc4b1xvuK\ndc2tR0VufWuUoytSTc3PRtC3n/cqsHwysOJrx747P3Qv8Dy04d+W7wRgvLKf47grYmPxVfI6pGe8\n7NrOhl7BYf4yZ7r5v9g43BV/MfAcOzFJyqb0tbSdQ03KX+3fE384vF82dUGj3DqbZwUkh9KcedqV\nx/Choi00rp7+P/SVNmBA63ALl22SMVTb1wygmeWWrtcGxF/UfYYK1T8Vs0GvzrbBun5zqPPs/OBR\nSpFv8574s+hEtZigDkWd5K2Fe9F2gbWIebmuYctJb3PBiXtr0cYDKtrgE+kXWbPXQ4lnLGmnKUAB\nOLBfZ0xUh3ruX652gxLSrTGlp8y2Zz390uV98oM33VCO1eP+v70zj4+quhf498xMZjJZSSCsARIM\nuyCQyKJhkyoErVKLr2gFFTWiRfSJUqjLo7Zqrc+F+mrVWp8LRZ6tvPd8aqUCb6k+qQUbNgEFAYEi\noLLDZLbTP+6d/c7MvRNjksn5fj755C7n3rn3lzO/nPM7v6U4L4dZYyrCVbRCzPlW6gRtyfDarDs7\nfNO0G0UfZtk/JElyljgNP0phQgtnisLR9n1rY6rfAHwS7MGhzulHrjlJFgCu9S5Ie2348202w6yS\ntqL0aQbicTns3H3xIH7j19LHbup6Oas37uYqxxo6kLy0YTIc9sizjdivLaIO9aw3dW3HghQlAVff\nb1gBKSVxnj7BxsSUyXf56q3dM46tK3/Nri9OMcGmLc4Xi1OG6ZXjEQLu8EZmCsIbmYEO8m/lGefj\nADjdyf9pXDmyJ9t+MoWepVo92b9FjaIvOhAZvMR7wsRz1+T+SaN9Ac6Qi1nRN+rOCvEz3gW+m8zd\nQCd6HcrhS5//PxlDyotxuGM9htzOzNShz5Y4on/Kbe29mpusV/SGyf+9kQ6y+4tTuPDyqjN15Cpo\n+T1C0XyG57EldOQTuHEa5EOPJ1m1pm1B87bwX8wYZmg6oiBFSts0nEYbrQSlxH/iUJrWyfnBxKoE\nd790Oe3NkH9qL387bG1Evudo7N/Q70lU9GafLaDnoL8v2qsIGLjlMSb+8/+EFaWdoKky9QLBimAk\nIjX6f0O1L1IjwZHCZVYIEZ5xnVVWkNy7Jo2it9sET189ImZRPprTuBjRq8TwXDwefUT/TOCSmOPF\npdb6piPKdHPq+NEULdPTaI+dFTmK0uePN8JvELz2x3yDsoUtSNYr+qWBC3ktMDb24J5IPusZz65l\nvuN3jLRtJx35TgcHU6zMSxJrzfpzihjfL31nTlaRyZci50o851V1oqJjbOdtCDYtsdIjM7TFwvzj\nO8n1Zx4IUuBycPGQ7jHH/tFnvijy8vrRhseF9LP11cWWniW+XFzD1kS3uqCJIJ5Hpg9laONznO15\njqVJsnOGFtUlguvOr7T0nKBlSTx43IM/EOTwyYjZxZ5vzp789NXVnGtLLBwC4ClPlm8/Qoc8JyfJ\n473A4IRzlc5jjKw056ly07g+TB7chVcDE8PHfNLOgrrE+6biqD3yeScPfZqiZXr2idj1EWen9C7D\nRpzyJQ6uchytJ0UxtANF36csn2MyVvmdOBUZwXX2fEq94834ywD4Xk3saNrttPOwfwY3e28zzF3j\nPrwhYUTtqBpvKgGS3S4SwuEBTmJtoccV57OfylfaDP27at4yI46uZNP2pvmI9+4YqzDyi8y7s51T\nbpy0yn36AHsParZ5s7Of+KjfOntsJPMxmUd9/a2k44qanpzCzUnDXPKw0PEKJUIzvYyqLOXSc7on\ntIknvqucafQx6sHV/NPrW2LjMUy69JXkG8cpVHiW0ViW3iY9pEcxRbkOikXirKc4YN5hoGOBi2dm\naoOGUCnGHBGgbog1s+J7rrEs9mkBidPs/w/ALO8PLd0jxM5jEWGf71liWInMDOVFidcZFVxvSVrX\n0zQDb982jp0y9gv28epIHpqbxWsx597VFdEZcnl4+tCE+wVsLv4QHEWDrEpQzHlfbU1Qq9sqzbls\n5eXYY8LhQ1jJvwGwyjckZv8p/6WWro8n2qI0df+S5A1NcMvEKtYGB4b3b75kjOlr401by/xaIqzC\nY9s5obuBzvbelXCdEUYRp9E87b+U8lLrC6fxzHH8V3g7WdBXPN2KY80AXs8ZXsh5mG4bf8k+mbkJ\nzggzawb5LgcbF0+mkMT4gkwXISfZ/prRdQC+IAneMn8JWiuqEyKPyGLufspMDciM2JxbExNvsCHY\nhzsnZ/ZMzUXWK3qnw5Ywoq8+pUXUrd/9FXXi/ZhzD/m/z0LfDczvlDi6htgR15cGeVXiR/QiWZRV\nHDab4P1FiVn8XrhupEHr5GwPdGeqnuPkksafsjJo7fp4fAEZ9to4y6bFCkxofDSje+Xl2HFERR8X\nlyWvhRuP3SZiXEcf9F8V3r5Nz3fyOeZmCA49je+OYHc+MFAS5WUllCYZCcez44E6Pn1wKh/8aBJT\nGn/GxCSyCeSYG4F3LHCxZv748P6AzY8wwb6BufKV8OxubOPjpu4VosZgpgiYXkgFWBFv/gTe6Xqj\npecAeGn2SMsxItF4AzIhX80ZA594MxR20hLg7Q2WcfkI830xntMyhx/7rwmnMV8f7Gd67eKbIusV\nPSQ3f6xb8/uEYzn4WR64gCPO9NNsEHwpYz1z7HGd2KSeB6BbsRu/jPxJtgZ7MaG/tQx4/oDkI1lB\nhWcZm2UfrhnTtHqUvkAwJpcHwG5p3YsHtH9mea7IlzS3yPy72QQ84I8EIhn9Tf93wSRT9wrYNMXw\nYbAvbwYSbf8XFZg3UTnsNmw2QeeiXLbJXuyS3VgZqElot3+A+WAciXHR7WvtKwFztUij+YJi9gYT\nZwP5LvN25CWBy2P+0d7hncOGrldYeg6Acf3KLK07xeMPBA2CnTIbie/IH87ljYsZ532cB6YNSX9B\nEkKfXud9mIsbH4wZhLQWmk3RCyGmCCG2CyF2CCEWNtfnmGHCEINFloAPVyAx5cG10zX7ocNurvNs\niFvsdMQlijI7ZQ8x07conHQpfopqBn/cMK3QRLWlVHQscDLQtje8vzPYLUXR7PQ4omyXebnmq16F\nptWhSkK/n5Mom56l5iIUD+b3Z473du71X8e/BSYknPd4rSaUi6XSoCD8meK+Bi2NKS9xc5H356wI\nxMr5bD0/0Io7rXl0LLtxFIv9sYn2Xrv5vKS5m4wRPOKPVGr7ikI6F2U2kt4Vl2vICnlOOzJOai+1\nJwAACPhJREFUbS2ZkdzXPxVF7hw+lP04r6oMtzPzxdN7LxnE7PMj2SzP7pm6vGJL0CyKXghhB34J\n1AGDgCuFEBaLln592PIiC3lhG/H6F6g6sTamXaVnKQVurfMnW0xZXj+aK0f2YttPpvDxT+tY7I91\nq6sn1uZ/6TAzM4MI7wcHc5XvHs7xPMuOvga50tPw40sH47TbeP7aGiYP7sLsWuueHtGUl+Txx0Ak\nOnLngJtSFs1OR6hO6fuBQRnZRCc2PsZM70KOnvYx3PN0+PiuoDXl8XZwJN8dVUXvLp2o8CyjtjGy\n/vDu0J9Zfq4QXYtyORU329gUrEBaWBR3OewEsLPQl2gaOSyL6d7JmlngvLM6sTpYzS3eeQAs8N1I\ndW9r91h1x7gYk8mkwT3Dys0q830381mwjLs6PWX52l9dXc3FUfWgNwUruGxYZmaX2ipNIS+cMjBN\ny9SUFbq479uD+La+2D5pQOvJQx+iuUb0I4EdUspPpZReYDlwWTN9VlpO5Gm2s5f8F7LIdwMnZS68\ndSe1xyOpdvcGy5DYGNmnlD5l+dxxoXHUY3XvUh66fAi5OXacDhu+ot7c75sZ9qeOZoTnaVwZulkd\no4DavtZHBtOG9+DjB+q4YEAXnplZY9rWnIp5vrk86ptOP8+LHOqTmNHQCm+6L+E/AudxhwXXyhCz\nxvRmP2X8KTiUcytLOUIRrwe0Bd238q0/V2XHfF6+XlvD2CfLGNv4OJWepQRzMstd8vrc83ljXi0L\nfPWsDQ5kTWAYt3jn8X3vjyzfa+Pii/CSw2fBMl71jw/PZCY0miuZaMRbwdFUeJbFuDiapapzIS/N\nHsm0xvtZEajlsmnTTcWHGOHBxTjvEk4Up070Z0T3Dm5mn18ZDmhb5LM+GAoxa0xv/rRgIkPKMx+4\nRHNFtWbzH97K7PNAE4xlqekB7I3a3weMStK22XG68qjwLAvvj218guEdTnPwmIfjuNkbNZUsys1h\nzfwJpu+9vH404x/x8Hygjh4cpos4wh7ZBS85YW8QK/xwygD++tkRaipKuGpU0+zrXxceXDwZ0BRp\npl/uEM68Dtz++VweveIcy9fef9nZXF9bSaM/SLFbG13O893KPN9crhxqXlahYiidi1x0LsplyuCu\nvL3l83A/mF5trsZwPEN1F9BPZDkzvPfGnDOTVTOaotwc3ri1lnFPajONe/yzsRPg1inW5QawZv54\nLnhUc0K4IsP369elkAZZRYOvip3uzBN52W2CQFAyqLu5XPbxVPcu4buBCfwuMCHjdwHNHGjW3GeG\ncf3KaLjvQjrkNX1w9XUjzLhYWb6pENOBKVLKG/T9mcAoKeXcqDb1QD1Ar169qvfsMV9I2ypfnGxk\n9IOrefLK4XQtzuXq5/7M+P5l+AKSdz46yLRh3SnIdXDhoK6mgpvi+df3drF66yHe3RFbRent28cy\noGtmnbk1sX7PEea/2kDnolyWXj+qScp+5+GTvLHhAPMmVWXszhaiYe9R5ry8nh4lbpbMGEZ5ibkv\nbTAoWb3tEN8a2Dn8DP5AkBff38OMc3uS72ra+Gfb58e57ZUGth88QacCJ+vuMQ6mSkcgKHli1ce4\nnXZWbz1EeYmbJ743LGO5fXmykX1HzjC4e1HMWokVlq7dQ2m+k6kW/d+j8fgCvPLBZ8waU5E0Ijwd\nqz46yNpPv+TOyf0t513KJoQQ66WUiav/8e2aSdGPARZLKSfr+4sApJQPGbWvqamR69atMzqlUCgU\niiSYVfTNZaP/C9BXCFEphHACM4DXm+mzFAqFQpGCZrHRSyn9Qoi5wErADjwvpdzSHJ+lUCgUitQ0\n12IsUsq3gNQVpBUKhULR7LSLyFiFQqFozyhFr1AoFFmOUvQKhUKR5ShFr1AoFFmOUvQKhUKR5TRL\nwJTlhxDiMNCU0NhOwBdpW7UvlEyMUXIxRsklkbYgk95Spq9I0yoUfVMRQqwzEx3WnlAyMUbJxRgl\nl0SySSbKdKNQKBRZjlL0CoVCkeVki6J/tqUfoBWiZGKMkosxSi6JZI1MssJGr1AoFIrkZMuIXqFQ\nKBRJaNOKvjUVIG8JhBC7hRCbhBANQoh1+rFSIcQ7QohP9N8lUe0X6bLaLoSY3HJP/vUhhHheCHFI\nCLE56phlGQghqnVZ7hBC/EI0tSpKC5NELouFEPv1/tIghJgadS7r5SKE6CmE+G8hxEdCiC1CiNv0\n49nfX6SUbfIHLf3xTqAP4AQ2AINa+rm+YRnsBjrFHfs5sFDfXgg8rG8P0mXkAip12dlb+h2+BhmM\nA0YAm5siA+ADYDQggD8AdS39bs0gl8XAnQZt24VcgG7ACH27EPhYf/es7y9teUTfqgqQtyIuA17U\nt18EpkUdXy6lbJRS7gJ2oMmwTSOl/D/gq7jDlmQghOgGFEkp10rtW/xS1DVtkiRySUa7kIuU8oCU\n8kN9+wSwFa2+ddb3l7as6I0KkPdooWdpKSSwSgixXq/BC9BFSnlA3/4cCFU+b0/ysiqDHvp2/PFs\n5FYhxEbdtBMyUbQ7uQghKoDhwJ9pB/2lLSt6BdRKKYcBdcAPhBDjok/qo4127ValZBDDr9BMncOA\nA8CjLfs4LYMQogB4DbhdSnk8+ly29pe2rOj3Az2j9sv1Y+0GKeV+/fch4N/RTDEH9akl+u9DevP2\nJC+rMtivb8cfzyqklAellAEpZRD4NRHTXbuRixAiB03J/1ZKuUI/nPX9pS0r+nZdgFwIkS+EKAxt\nAxcBm9FkcI3e7BrgP/Xt14EZQgiXEKIS6Iu2oJSNWJKBPm0/LoQYrXtPzIq6JmsIKTOd76D1F2gn\nctHf4TfAVinlY1Gnsr+/tPRqcFN+gKloK+c7gbtb+nm+4Xfvg+YRsAHYEnp/oCOwGvgEWAWURl1z\nty6r7bRyLwELcngFzQzhQ7OVXp+JDIAaNMW3E/gX9GDCtvqTRC4vA5uAjWhKrFt7kgtQi2aW2Qg0\n6D9T20N/UZGxCoVCkeW0ZdONQqFQKEygFL1CoVBkOUrRKxQKRZajFL1CoVBkOUrRKxQKRZajFL1C\noVBkOUrRKxQKRZajFL1CoVBkOX8HBtYysWLXYjUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ec69d1dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# line plot of observed vs predicted\n",
    "pyplot.plot(raw_values[-2184:])\n",
    "pyplot.plot(predictions)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2820,)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_values.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2184\n"
     ]
    }
   ],
   "source": [
    "print(len(predictions))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}