Alpha_RNNs-Bitcoin.ipynb

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    "# Alpha_RNNs-Bitcoin\n",
    "# Author: Matthew Dixon\n",
    "# Version: 1.1 (27.2.2020)\n",
    "# License: MIT\n",
    "# Email: matthew.dixon@iit.edu\n",
    "# Notes: tested on Mac OS X with Python 3.6 and Tensorflow 1.3.0\n",
    "# Citation: Please cite the following reference if this notebook is used for research purposes:\n",
    "# M.F Dixon, Industrial Forecasting with Exponentially Smoothed Recurrent Neural Networks, preprint, 2020."
   ]
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   "source": [
    "## An Introduction to Prediction with RNNs\n",
    "\n",
    "### Overview\n",
    "- This notebook provides an example of how Keras can be used to train and test RNNs for time series prediction. The example dataset is for predicting from noisy non-stationarity data.\n",
    "- Statistical methods used for autoregressive models shall be used to identify the sequence length needed in the RNN and to diagnose the model error.\n",
    "- Plain RNNs are not suited to non-stationary time series modeling. We can use a GRU or LSTM to model non-stationarity data, since these models exhibit dynamic auto-correlation structure.\n",
    "- Unlike classical time series methods, e.g. ARIMA, there are no parameteric assumptions on the distribution of the errors, and non-linear relationships between response and predictors can be captured. \n",
    "- The data is one minute snapshots of the USD value of coinbase over 2018."
   ]
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   "source": [
    "#### Statistician's note\n",
    "- We choose to build a model which provides strong predictive power, in favor of explantory power. \n",
    "- Our choice to use a recurrent neural network is predicated on each observation in the time series being dependent on previous observations. The ordering of the observations therefore matters and $X$ is not iid.\n",
    "- Once the input data is appropriately scaled, model building starts with 'feature selection' -identifying the relevant features to include in the model. \n",
    "- In this notebook, we assume that we've already identifed the relevant set of features (i.e. there is only one time series provided).\n",
    "- Our primary concern in assessing the extent to which the model is over-fitting by comparing the in and out-of-sample MSEs.\n",
    "\n",
    "#### Implementation notes\n",
    "- It is important to ensure that shuffle=False in the fit function, otherwise the ordering of sequences is not preserved. This is especially important for methods which have memory beyond the current sequence (i.e. all methods except RNNs).\n",
    "- Time series cross-validation must be used for hyper-parameter tuning because the ordering of the data matters. In particular, the model can not use training data more recent than the forecasting observation date."
   ]
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     "text": [
      "Go to this URL in a browser: https://accounts.google.com/o/oauth2/auth?client_id=947318989803-6bn6qk8qdgf4n4g3pfee6491hc0brc4i.apps.googleusercontent.com&redirect_uri=urn%3aietf%3awg%3aoauth%3a2.0%3aoob&response_type=code&scope=email%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdocs.test%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdrive%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdrive.photos.readonly%20https%3a%2f%2fwww.googleapis.com%2fauth%2fpeopleapi.readonly\n",
      "\n",
      "Enter your authorization code:\n",
      "··········\n",
      "Mounted at /content/drive\n"
     ]
    }
   ],
   "source": [
    "#Only needed if the notebook is being run on Google Golab\n",
    "from google.colab import drive\n",
    "drive.mount('/content/drive', force_remount=True)"
   ]
  },
  {
   "cell_type": "code",
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    "id": "rJlPU1uBtN59"
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   "outputs": [],
   "source": [
    "import sys\n",
    "path = '/content/drive/My Drive/alpha-RNN' # set the path to location of the data file coinbase.csv\n",
    "sys.path.append(path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
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    "colab": {},
    "colab_type": "code",
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "import tensorflow as tf\n",
    "import statsmodels.api as sm\n",
    "import os\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.model_selection import TimeSeriesSplit\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "from keras import optimizers\n",
    "from keras.callbacks import EarlyStopping\n",
    "from keras.models import Sequential\n",
    "from keras.models import load_model\n",
    "from keras.layers import Dense\n",
    "from keras.layers import Layer, LSTM, GRU, SimpleRNN\n",
    "from keras import optimizers\n",
    "from keras.regularizers import l1,l2\n",
    "from keras import regularizers\n",
    "from keras.wrappers.scikit_learn import KerasClassifier, KerasRegressor\n",
    "from keras.layers import Layer,RNN\n",
    "from keras import backend as K\n",
    "from keras import layers\n",
    "import keras.layers\n",
    "from keras.legacy import interfaces\n",
    "from keras import *\n",
    "# Custom classes for alpha-RNNs and alpha_t-RNNs\n",
    "from alphaRNN import *\n",
    "from alphatRNN import *"
   ]
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  {
   "cell_type": "code",
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   "source": [
    "%matplotlib inline"
   ]
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   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "g5QbSSsmqjvF"
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   "source": [
    "### Example Data\n",
    "- The example dataset is a chronologically ordered time series. The ordering of the observations matters and each observation is not assumed to be independent (as with cross-sectional classification data). \n",
    "\n",
    "- Each observation $X$ has one variable (a.k.a. univariate time series)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ojxc_gL-qjvJ"
   },
   "source": [
    "Loading the Pandas Dataframe, viewing the first ten rows and the distribution of the labels:"
   ]
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  {
   "cell_type": "code",
   "execution_count": 0,
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    "colab": {},
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    "id": "u1OUq236qjvN"
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   "outputs": [],
   "source": [
    "df = pd.read_csv(path + '/coinbase.csv', index_col=[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>USD</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>timestamp</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-01-01 00:00:00</th>\n",
       "      <td>13598.814422</td>\n",
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       "    <tr>\n",
       "      <th>2018-01-01 00:01:00</th>\n",
       "      <td>13596.912824</td>\n",
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       "    <tr>\n",
       "      <th>2018-01-01 00:02:00</th>\n",
       "      <td>13568.356998</td>\n",
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       "    <tr>\n",
       "      <th>2018-01-01 00:03:00</th>\n",
       "      <td>13560.425182</td>\n",
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       "    <tr>\n",
       "      <th>2018-01-01 00:04:00</th>\n",
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       "                              USD\n",
       " timestamp                       \n",
       "2018-01-01 00:00:00  13598.814422\n",
       "2018-01-01 00:01:00  13596.912824\n",
       "2018-01-01 00:02:00  13568.356998\n",
       "2018-01-01 00:03:00  13560.425182\n",
       "2018-01-01 00:04:00  13552.270931"
      ]
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   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Xp8DNh3Lqjvj"
   },
   "source": [
    "# RNN Regression\n",
    "We consider a univariate prediction problem where the time series is given by 'USD' in the data frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
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   "source": [
    "use_features = ['USD'] # continuous input\n",
    "target = 'USD' # continuous output"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### Stationarity\n",
    "It is essential to determine whether the time series is \"stationary\". Informally, stationarity is when the auto-covariance is independent of time. Failure to establish stationarity will almost certainly lead to misinterpretation of model identification and diagnostics tests. Moreover, stationarity is decisive in characterizing the prediction problem and whether to use a more advanced architecture. In particular, we can expect a plain RNN to perform poorly if the data is non-stationary as the RNN exhibits fixed auto-covariance. \n",
    "\n",
    "We perform an Augmented Dickey-Fuller test to establish stationarity under the assumption that the time series has a constant bias but does not exhibit a time trend. In other words, we assume that the time series is already de-trended. \n",
    "\n",
    "If the stationarity test fails, even after first de-trending the time series, then one potential recourse is to simply take differences of time series and predict $\\Delta y_t$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "id": "azMbPKuXqjv1"
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   "source": [
    "The null hypothesis of the Augmented Dickey-Fuller is that there is a unit root, with the alternative that there is no unit root. If the p-value is above $(1-\\alpha)$, then we cannot reject that there is a unit root. Note that a subset of the time series is used to reduce the memory requirements of the test. We use the first 200000 samples to test for stationarity. While the test statistic is sensitive to the data size, the ADF test is always accepted at the 99\\% level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "gUXzLXEoqjv5"
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   "outputs": [],
   "source": [
    "df=df.fillna(method=\"backfill\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "V_DF3IABqjwA"
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   "outputs": [],
   "source": [
    "adf, p, usedlag, nobs, cvs,aic=sm.tsa.stattools.adfuller(df[use_features[0]][:200000].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "wLjxzajyqjwJ"
   },
   "outputs": [],
   "source": [
    "print(adf,p, nobs, cvs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jxx3NIqxqjwT"
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   "source": [
    "Here we accept the null as the p-value is larger than 0.01, thus we can not reject the test at the 99% confidence level. This suggests that the time series is non-stationary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6Vo_X2UDqjwV"
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   "source": [
    "#### Autoregressive Model Identification: The partial auto-correlation\n",
    "It is important to determine the number of lags, the sequence length, required in the RNN by statistical analysis. A brute-force approach will in general be too time consuming.\n",
    "\n",
    "A partial auto-correlation at lag $h\\geq 2$ is a conditional auto-correlation between a variable, $X_t$, and its $h^{th}$ lag, $X_{t-h}$ under the assumption that we control for the values of the intermediate lags, $X_{t-1},\\dots, X_{t-h+1}$:\n",
    "\n",
    "$$\\tau_h:=\\tau(X_t, X_{t-h}; X_{t-1},\\dots, X_{t-h+1}):=\\frac{\\gamma(X_t, X_{t-h}; X_{t-1},\\dots, X_{t-h+1})}{\\sqrt{\\gamma(X_t |X_{t-1},\\dots, X_{t-h+1})\\gamma(X_{t-h} |X_{t-1},\\dots, X_{t-h+1}))}},\n",
    "$$ \n",
    "where $\\gamma_h:=\\gamma(X_tX_{t-h})$ is the lag-$h$ autocovariance. The partial autocorrelation function $\\tau_h:\\mathbb{N} \\rightarrow [-1,1]$ is a map $h:\\mapsto \\tau_h$.\n",
    "\n",
    "The estimated partial auto-correlation function (PACF) can be used to identify the order of an autoregressive time series model. Values of $|\\tau_h|$ greater or equal to $\\frac{\\Phi^{-1}(\\alpha)}{\\sqrt{T}}$, where T is the number of observations and $\\Phi(z)$ is the standard normal CDF, are significant lag $h$ partial autocorelations at the $\\alpha$ confidence level.\n",
    "\n",
    "We use the stattools package to estimat the PACF. The 'nlags' parameter is the maximum number of lags used for PACF estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
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    "colab_type": "code",
    "id": "MKLHw7tqqjwY"
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   "outputs": [],
   "source": [
    "pacf=sm.tsa.stattools.pacf(df[use_features], nlags=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RsQTxSq5qjwf"
   },
   "source": [
    "We find the first lag which isn't significant at the 99% level and automatically determine the number of lags needed in our autoregressive model as one below this value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
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    "colab_type": "code",
    "id": "xzsy_bjyqjwh"
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   "outputs": [],
   "source": [
    "n_steps=np.where(np.array(np.abs(pacf)>2.58/np.sqrt(len(df[use_features])))==False)[0][0] -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
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    "colab_type": "code",
    "id": "kQXc5W6iqjwp",
    "outputId": "cc98e2c9-3832-4a29-8360-025e029ea808"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "print(n_steps)"
   ]
  },
  {
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    "id": "Fnv19w5tqjwy"
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   "source": [
    "This may lead to a high order model, with more lags than strictly necessary. We could view this value, informally, as an upper bound on the number of lags needed. We can also simply identify the order of the model based on the plot of the PACF. In this case, a minimum of 4 lags appears satisfactory, although more may be needed. Unlike autoregressive models, the advantage of using fewer parameters is purely computational as adding more lags does not increase the number of parameters, only the size of the tensorial representation of the sequence data in TensorFlow. "
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Idm5ubhKqVnM2r60xxmnO6oe2InILkAXMjrdeVeepapaqZrVr1+5sVu0Mfp+H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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pacf, label='pacf')\n",
    "plt.plot([2.58/np.sqrt(len(df[use_features]))]*30, label='99% confidence interval (upper)')\n",
    "plt.plot([-2.58/np.sqrt(len(df[use_features]))]*30, label='99% confidence interval (lower)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jHSnkymxqjw7"
   },
   "source": [
    "Split the training and test set by using the first 80% of the time series and the remaining 20% for the test set. Note that the test set must be in the future of the training set to avoid look-ahead bias. Also, random sampling of the data can not be used as this would eliminate the auto-correlation structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Y7D1y9USqjw9"
   },
   "outputs": [],
   "source": [
    "train_weight = 0.8\n",
    "split = int(len(df)*train_weight)\n",
    "df_train = df.iloc[:split]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "JB3yo5YkqjxE"
   },
   "source": [
    "### Scaling\n",
    "Standardization of the data is important to avoid potential scaling difficulties in the fitting of the model. When there is more than one feature (covariate), scaling avoids one feature dominating over another due to disparate scales.\n",
    "\n",
    "To avoid introducing a look-ahead bias into the prediction, we must re-scale the training data without knowledge of the test set. Hence, we will simply standardize the training set using the mean and standard deviation of the training set and not the whole time series. Additionally, to avoid introducing a systematic bias into test set, we use the identical normalization for the test set - the mean and standard deviation of the training set are used to normalize the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "J2GbNeZ4qjxG"
   },
   "outputs": [],
   "source": [
    "mu = np.float(df_train[use_features].mean())\n",
    "sigma = np.float(df_train[use_features].std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "JxQ09iVxqjxL"
   },
   "outputs": [],
   "source": [
    "df_train = df_train[use_features].apply(lambda x: (x - mu) / sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "frBSJqDaqjxS"
   },
   "outputs": [],
   "source": [
    "df_test = df.iloc[split:]\n",
    "df_test = df[use_features].apply(lambda x: (x - mu) / sigma).iloc[split:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ooDbr1Giqjxa"
   },
   "source": [
    "### Data formatting for RNNs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "80KLxffJqjxd"
   },
   "source": [
    "TensorFlow uses tensors to represent data. To perform sequence learning, the time series of variables must be transformed to a series of over-lapping sub-sequences. \n",
    "\n",
    "For example, consider a univariate time series of increasing integers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fk_D3SrKqjxe"
   },
   "source": [
    "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "avKQL4MWqjxg"
   },
   "source": [
    "Setting the sequence length to 10, for example, we move the window forward by one observation at a time and construct new sequences:\n",
    "\n",
    "1 2 3 4 5 6 7 8 9 10\n",
    "\n",
    "2 3 4 5 6 7 8 9 10 11\n",
    "\n",
    "3 4 5 6 7 8 9 10 11 12\n",
    "\n",
    "4 5 6 7 8 9 10 11 12 13\n",
    "\n",
    "5 6 7 8 9 10 11 12 13 14\n",
    "\n",
    "6 7 8 9 10 11 12 13 14 15\n",
    "\n",
    "\n",
    "Let's define the following function for reshaping the data into one-step ahead times series prediction format. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "YPCndJ8sqjxj"
   },
   "outputs": [],
   "source": [
    "def get_lagged_features(value, n_steps, n_steps_ahead):\n",
    "    \"\"\"\n",
    "    value: feature value to be lagged\n",
    "    n_steps: number of lags, i.e. sequence length\n",
    "    n_steps_ahead: forecasting horizon\n",
    "    \"\"\"\n",
    "    lag_list = []\n",
    "    for lag in range(n_steps+n_steps_ahead-1, n_steps_ahead-1, -1):\n",
    "        lag_list.append(value.shift(lag))\n",
    "    return pd.concat(lag_list, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gOk1scB1qjxn"
   },
   "source": [
    "We shall first transform the training input and output data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mMP_lraNqjxq"
   },
   "outputs": [],
   "source": [
    "n_steps_ahead=4\n",
    "\n",
    "x_train_list = []\n",
    "for use_feature in use_features:\n",
    "    x_train_reg = get_lagged_features(df_train, n_steps, n_steps_ahead).dropna()\n",
    "    x_train_list.append(x_train_reg)\n",
    "x_train_reg = pd.concat(x_train_list, axis=1)\n",
    "\n",
    "col_ords = []\n",
    "for i in range(n_steps):\n",
    "    for j in range(len(use_features)):\n",
    "        col_ords.append(i + j * n_steps)\n",
    "\n",
    "x_train_reg = x_train_reg.iloc[:, col_ords]\n",
    "y_train_reg = df_train.loc[x_train_reg.index, [target]].values\n",
    "x_train_reg = np.reshape(x_train_reg.values, (x_train_reg.shape[0], np.int(x_train_reg.shape[1] / len(use_features)), len(use_features)))\n",
    "y_train_reg = np.reshape(y_train_reg, (y_train_reg.shape[0], 1, 1))\n",
    "\n",
    "x_test_list = []\n",
    "for use_feature in use_features:\n",
    "    x_test_reg = get_lagged_features(df_test, n_steps,n_steps_ahead).dropna()\n",
    "    x_test_list.append(x_test_reg)\n",
    "x_test_reg = pd.concat(x_test_list, axis=1)\n",
    "\n",
    "x_test_reg = x_test_reg.iloc[:, col_ords]\n",
    "y_test_reg = df_test.loc[x_test_reg.index, [target]].values\n",
    "x_test_reg = np.reshape(x_test_reg.values, (x_test_reg.shape[0], np.int(x_test_reg.shape[1]/len(use_features)), len(use_features)))\n",
    "\n",
    "y_test_reg = np.reshape(y_test_reg, (y_test_reg.shape[0], 1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "av-Dyaweqjxw"
   },
   "source": [
    "Print the shapes of each tensor. The first digit is the number of observations. For feature arrays, the second digit is the sequence length (i.e. the number of lags in the model) and the final digit is the dimension of each element in the sequence or output vector respectively. In this case, the example performs univariate time series analysis and so the dimension of the input and output is 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "VbIMhSYYqjxx",
    "outputId": "01222a29-7331-4520-f2c8-9d3f3f141a51"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(361337, 4, 1) (361337, 1, 1) (90330, 4, 1) (90450, 1, 1)\n"
     ]
    }
   ],
   "source": [
    "print(x_train_reg.shape,y_train_reg.shape,x_test_reg.shape,y_test_reg.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "T870gAP2qjx3"
   },
   "outputs": [],
   "source": [
    "train_batch_size = y_train_reg.shape[0]\n",
    "test_batch_size = y_test_reg.shape[0]\n",
    "time_size = y_train_reg.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "MgJidF_6qjx9"
   },
   "outputs": [],
   "source": [
    "x_train_reg = pd.concat(x_train_list, axis=1)\n",
    "x_train_reg = x_train_reg.iloc[:, col_ords]\n",
    "y_train_reg = df_train.loc[x_train_reg.index, [target]].values\n",
    "x_train_reg = np.reshape(x_train_reg.values, (x_train_reg.shape[0], np.int(x_train_reg.shape[1] / len(use_features)), len(use_features)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AsUwPwYhqjyF"
   },
   "outputs": [],
   "source": [
    "x_test_reg = pd.concat(x_test_list, axis=1)\n",
    "x_test_reg = x_test_reg.iloc[:, col_ords]\n",
    "y_test_reg = df_test.loc[x_test_reg.index, [target]].values\n",
    "x_test_reg = np.reshape(x_test_reg.values, (x_test_reg.shape[0], np.int(x_test_reg.shape[1]/len(use_features)), len(use_features)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aieEXctCqjyK"
   },
   "source": [
    "### Model Specification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "tBFnFLZZqjyM"
   },
   "outputs": [],
   "source": [
    "def AlphatRNN_(n_units = 10, l1_reg=0, seed=0):\n",
    "  model = Sequential()\n",
    "  model.add(AlphatRNN(n_units, activation='tanh', recurrent_activation='sigmoid', kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), recurrent_initializer=keras.initializers.orthogonal(seed), kernel_regularizer=l1(l1_reg), input_shape=(x_train_reg.shape[1], x_train_reg.shape[-1]), unroll=True))  \n",
    "  model.add(Dense(1, kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), kernel_regularizer=l1(l1_reg)))\n",
    "  model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "  return model\n",
    "\n",
    "\n",
    "def AlphaRNN_(n_units = 10, l1_reg=0, seed=0):\n",
    "  model = Sequential()\n",
    "  model.add(AlphaRNN(n_units, activation='tanh', kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), recurrent_initializer=keras.initializers.orthogonal(seed), kernel_regularizer=l1(l1_reg), input_shape=(x_train_reg.shape[1], x_train_reg.shape[-1]), unroll=True))\n",
    "  model.add(Dense(1, kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), kernel_regularizer=l1(l1_reg)))\n",
    "  model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "  return model\n",
    "\n",
    "\n",
    "def SimpleRNN_(n_units = 10, l1_reg=0, seed=0):\n",
    "  model = Sequential()\n",
    "  model.add(SimpleRNN(n_units, activation='tanh', kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), recurrent_initializer=keras.initializers.orthogonal(seed), kernel_regularizer=l1(l1_reg), input_shape=(x_train_reg.shape[1], x_train_reg.shape[-1]), unroll=True, stateful=False))  \n",
    "  model.add(Dense(1, kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), kernel_regularizer=l1(l1_reg)))\n",
    "  model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "  return model\n",
    "\n",
    "\n",
    "def GRU_(n_units = 10, l1_reg=0, seed=0):\n",
    "  model = Sequential()\n",
    "  model.add(GRU(n_units, activation='tanh', kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), recurrent_initializer=keras.initializers.orthogonal(seed), kernel_regularizer=l1(l1_reg), input_shape=(x_train_reg.shape[1], x_train_reg.shape[-1]), unroll=True))  \n",
    "  model.add(Dense(1, kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), kernel_regularizer=l1(l1_reg)))\n",
    "  model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "  return model\n",
    "\n",
    "\n",
    "def LSTM_(n_units = 10, l1_reg=0, seed=0):\n",
    "  model = Sequential()\n",
    "  model.add(LSTM(n_units, activation='tanh', kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), recurrent_initializer=keras.initializers.orthogonal(seed), kernel_regularizer=l1(l1_reg), input_shape=(x_train_reg.shape[1], x_train_reg.shape[-1]), unroll=True)) \n",
    "  model.add(Dense(1, kernel_initializer=keras.initializers.glorot_uniform(seed), bias_initializer=keras.initializers.glorot_uniform(seed), kernel_regularizer=l1(l1_reg)))\n",
    "  model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "  return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0Bmr9nNVqjyR"
   },
   "outputs": [],
   "source": [
    "max_epoches=2000\n",
    "batch_size=1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KGCWFF1-qjyW"
   },
   "source": [
    "Use a batch size of 1000 as the dataset is reasonably large and the training time would be too long otherwise. 20 epoches have been used here, but a better approach would be to use a stopping criteria through a call back. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "SrDjZpVdqjyZ"
   },
   "outputs": [],
   "source": [
    "es = EarlyStopping(monitor='loss', mode='min', verbose=1, patience=100, min_delta=1e-7, restore_best_weights=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jr_42Ab_qjye"
   },
   "outputs": [],
   "source": [
    "params = {'rnn': {'model':'', 'function':SimpleRNN_, 'l1_reg':0.0, 'H':20, 'color': 'blue', 'label':'RNN'}, \n",
    "          'alpharnn': {'model':'', 'function':AlphaRNN_,'l1_reg':0.0, 'H':10,'color': 'green', 'label': '$\\\\alpha$-RNN' }, \n",
    "          'alphatrnn': {'model':'', 'function':AlphatRNN_,'l1_reg':0.0, 'H':5, 'color': 'cyan', 'label': '$\\\\alpha_t$-RNN'},\n",
    "          'gru': {'model':'', 'function':GRU_,'l1_reg':0.0, 'H':10, 'color': 'orange', 'label': 'GRU'},\n",
    "          'lstm': {'model':'', 'function':LSTM_,'l1_reg':0.0, 'H':10, 'color':'red', 'label': 'LSTM'}\n",
    "         }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "oKcoWfmHqjyi"
   },
   "source": [
    "# Cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "dM8rOT-rqjyj"
   },
   "outputs": [],
   "source": [
    "cross_val=False # Warning: Changing this to True will take several hours to run\n",
    "if cross_val:\n",
    "    n_units = [5,10,20]\n",
    "    l1_reg = [0, 0.001, 0.01, 0.1]\n",
    "    tscv = TimeSeriesSplit(n_splits = 5)\n",
    "    param_grid = dict(n_units=n_units,l1_reg=l1_reg)\n",
    "\n",
    "    for key in params.keys(): # params[key]['function']\n",
    "        model = KerasRegressor(build_fn=params[key]['function'], epochs=max_epoches, batch_size=batch_size, verbose=2)\n",
    "        grid = GridSearchCV(estimator=model,param_grid=param_grid, cv=tscv, n_jobs=1, verbose=2)\n",
    "        grid_result = grid.fit(x_train_reg[:30000],y_train_reg[:30000],callbacks=[es])\n",
    "        print(\"Best: %f using %s\" % (grid_result.best_score_, grid_result.best_params_))\n",
    "        means = grid_result.cv_results_['mean_test_score']\n",
    "        stds = grid_result.cv_results_['std_test_score']\n",
    "        params_ = grid_result.cv_results_['params']\n",
    "        for mean, stdev, param_ in zip(means, stds, params_):\n",
    "            print(\"%f (%f) with %r\" % (mean, stdev, param_))\n",
    "\n",
    "        params[key]['H'] = grid_result.best_params_['n_units']\n",
    "        params[key]['l1_reg']= grid_result.best_params_['l1_reg']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BqEXCGyoqjyo"
   },
   "source": [
    "# Train cross-validated model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "A0FpTqNWqjyq"
   },
   "outputs": [],
   "source": [
    "for key in params.keys():\n",
    "    tf.set_random_seed(0)\n",
    "    model=params[key]['function'](params[key]['H'],params[key]['l1_reg'])\n",
    "    model.fit(x_train_reg,y_train_reg,epochs=max_epoches, batch_size=batch_size,callbacks=[es],shuffle=False)\n",
    "    params[key]['model']=model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "tQmA1vK1mbCM"
   },
   "outputs": [],
   "source": [
    "# optionally save the fitted model\n",
    "for key in params.keys():\n",
    "  params[key]['model'].save(key + '.hdf5', overwrite=True)  # creates a HDF5 file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZyLz5ik1ANCv"
   },
   "outputs": [],
   "source": [
    "# optionally load the fitted model\n",
    "for key in params.keys():\n",
    "  params[key]['model']=load_model(key + '.hdf5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "a9OE7I07dEhV"
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return (1 / (1 + np.exp(-x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "fC3xzTJ4cHG4",
    "outputId": "1e84ce92-289c-4e07-fe25-c3f5b4a01926"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha= [0.32280117]\n"
     ]
    }
   ],
   "source": [
    "model = params['alpharnn']['model']\n",
    "names = [weight.name for layer in model.layers for weight in layer.weights]\n",
    "weights = model.get_weights()\n",
    "\n",
    "for name, weight in zip(names, weights):\n",
    "    if name =='alpha_rnn_1/alpha:0':\n",
    "      print(\"alpha= \" + str(sigmoid(weight)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "y1gZjjPgqjy3"
   },
   "source": [
    "### Prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aEhlyKjSqjy4"
   },
   "source": [
    "We shall now apply the fitted RNN model to the training set and the test set, separately. We can then informally assess the extent\n",
    "of over-fitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "t3a1F-Y8qjy5",
    "outputId": "c183b29d-0f1b-48b0-859d-27e73ac8f919"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_1\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "simple_rnn_1 (SimpleRNN)     (None, 20)                440       \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 1)                 21        \n",
      "=================================================================\n",
      "Total params: 461\n",
      "Trainable params: 461\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "361337/361337 [==============================] - 6s 17us/step\n",
      "90330/90330 [==============================] - 1s 16us/step\n",
      "Model: \"sequential_2\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "alpha_rnn_1 (AlphaRNN)       (None, 10)                121       \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 1)                 11        \n",
      "=================================================================\n",
      "Total params: 132\n",
      "Trainable params: 132\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "361337/361337 [==============================] - 6s 18us/step\n",
      "90330/90330 [==============================] - 2s 18us/step\n",
      "Model: \"sequential_3\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "alphat_rnn_1 (AlphatRNN)     (None, 5)                 80        \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 1)                 6         \n",
      "=================================================================\n",
      "Total params: 86\n",
      "Trainable params: 86\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "361337/361337 [==============================] - 7s 20us/step\n",
      "90330/90330 [==============================] - 2s 20us/step\n",
      "Model: \"sequential_4\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "gru_1 (GRU)                  (None, 10)                360       \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 1)                 11        \n",
      "=================================================================\n",
      "Total params: 371\n",
      "Trainable params: 371\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "361337/361337 [==============================] - 9s 24us/step\n",
      "90330/90330 [==============================] - 2s 24us/step\n",
      "Model: \"sequential_5\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "lstm_1 (LSTM)                (None, 10)                480       \n",
      "_________________________________________________________________\n",
      "dense_5 (Dense)              (None, 1)                 11        \n",
      "=================================================================\n",
      "Total params: 491\n",
      "Trainable params: 491\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "361337/361337 [==============================] - 9s 25us/step\n",
      "90330/90330 [==============================] - 2s 26us/step\n"
     ]
    }
   ],
   "source": [
    "for key in params.keys():\n",
    "  model=params[key]['model']\n",
    "  model.summary()\n",
    "    \n",
    "  params[key]['MSE_train']= mean_squared_error(df_train[use_feature][n_steps+n_steps_ahead-1:],model.predict(x_train_reg, verbose=1))\n",
    "  params[key]['predict'] = model.predict(x_test_reg, verbose=1) \n",
    "  params[key]['MSE_test']= mean_squared_error(df_test[use_feature][n_steps+n_steps_ahead-1:],params[key]['predict'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "I99U7i80qjy-"
   },
   "source": [
    "### Model Performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OjslcI9Aqjy_"
   },
   "source": [
    "We observe the in-sample prediction is reliable (upper plot). Most of the out-of-sample prediction (lower plot) is also reliable although the end of the predicted sequence appears to degrade. Such a degradation indicates the prediction horizon might be too long and the model should be retrained."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "J_ADoAkeqjzB"
   },
   "source": [
    "Finally assess the performance of the model in and out-of-sample using the MSE. We expect the mean error to be larger on the test set than on the training set. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 556
    },
    "colab_type": "code",
    "id": "f67u-snqqjzD",
    "outputId": "ca4f8a64-3780-4cc1-a3f5-b738606f5c77"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rnn\n",
      "alpharnn\n",
      "alphatrnn\n",
      "gru\n",
      "lstm\n"
     ]
    },
    {
     "data": {
      "image/png": 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dd+ckheXkqmX9xZc8xoHsuUB0oKsjhBBC/GNhYWG8//77buuWLFly0n127dpV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qahBw18aYkDuOUHCunaM0ecCcCBPQ80VzaBHmxxE/UE+gD/hHWPdGdhipCDva3kHqYYb/Jf5QRa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\nOHBb3XAjMB26tVFvQ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oiomITa2+MfN9DolinCEp55xuzjjYiStGdUoK7r2Frsr9G7mb4Z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\n4P8DGS20ovvltU4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,7))\n",
    "upper = 2000\n",
    "plt.plot(df_test.index[n_steps+n_steps_ahead-1:upper], df_test[use_feature][n_steps+n_steps_ahead-1:upper], color=\"black\", label=\"Observed\")\n",
    "\n",
    "for key in params.keys():\n",
    "  print(key)\n",
    "  plt.plot(df_test.index[n_steps+n_steps_ahead-1:upper], params[key]['predict'][:upper-(n_steps+n_steps_ahead-1), 0], color=params[key]['color'], label=params[key]['label'])\n",
    "plt.legend(loc=\"best\", fontsize=12)\n",
    "plt.xlabel('Time', fontsize=20)\n",
    "plt.ylabel('Y', fontsize=20)\n",
    "plt.title('Observed vs Model (Testing)', fontsize=16)\n",
    "\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 469
    },
    "colab_type": "code",
    "id": "XSX5YYRCqjzH",
    "outputId": "99f4a429-9643-4e42-ea49-8efa6bf190df"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MGMDQoUPDbh89ejR///vf2bSp+AEVkdQBaN68OatXr47gU0UmNzc3eFf+448/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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,7))\n",
    "\n",
    "for key in params.keys():\n",
    "   plt.plot(df_test.index[n_steps+n_steps_ahead-1:upper], df_test[use_feature][n_steps+n_steps_ahead-1:upper]-params[key]['predict'][:upper-(n_steps+n_steps_ahead-1), 0], color=params[key]['color'], label=params[key]['label'] + \" (\" +  str(round(params[key]['MSE_test'],7)) +\")\")\n",
    "\n",
    "plt.legend(loc=\"best\", fontsize=12)\n",
    "plt.title('Observed vs Model Error (Training)', fontsize=16)\n",
    "plt.xlabel('Time', fontsize=20)\n",
    "plt.ylabel('Y-$\\hat{Y}$', fontsize=20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "6c_adfrzqjzM"
   },
   "source": [
    "### Model Diagnostics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UGHvu0xVqjzO"
   },
   "source": [
    "A fitted time series model must be examined for underfitting with a white noise test. We analyze the model residuals (i.e. the error $u_t$) to determine whether it is white noise or whether it is auto-correlated. The latter case provides statistical evidence that more lags are needed in the RNN. Box and Pierce propose the Portmanteau statistic:\n",
    "\n",
    "$$Q^*(m)=T\\sum_{l=1}^m\\hat{\\tau}_l^2,$$\n",
    "\n",
    "as a test statistic for the null hypothesis $$H_0:\\tau_1=\\dots=\\tau_m=0$$ against the alternative hypothesis $$H_a:\\tau_i\\neq 0$$ for some $$i\\in\\{1,\\dots,m\\}$$, where $T$ is the number of observations, $\\hat{\\tau}_i$ are the sample autocorrelations of the residual, and $m$ is the maximum lag used in the test. There are several heuristics in the statistics literature to determine the maximum lag such as the Schwert statistic. \n",
    "\n",
    "The Box-Pierce statistic follows an asymptotically chi-squared distribution with $m$ degrees of freedom.\n",
    "\n",
    "The Ljung-Box test statistic increases the power of the test in finite samples:\n",
    "$$Q(m)=T(T+2)\\sum_{l=1}^m\\frac{\\hat{\\tau}_l^2}{T-l}$$.\n",
    "\n",
    "This statistic also follows an asymptotically chi-squared distribution with $m$ degrees of freedom. The decision rule is to reject $H_0$ if $Q(m)>\\chi_{\\alpha}^2$ where $\\chi_{\\alpha}^2$ denotes the $100(1-\\alpha)^{th}$ percentile of a chi-squared distribution with m degrees of freedom and is the significance level for rejecting $H_0$.\n",
    "\n",
    "The test can be time consuming and we select a subset of the residuals. Here we simply set the maximum lag to 20. In the results below, we find that the p-values are all smaller than 0.01, indicating that we can reject the null at the 99% confidence level for any lag. This is strong evidence that the model is under-fitting and more lags are needed in our model. Unlike an auto-regressive model, increasing the number of lags in the RNN does not increase the number of weights. Thus there is no danger of over-fitting by increasing the lag, although there will be an increase in the training time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7bpznKjiqjzQ"
   },
   "outputs": [],
   "source": [
    "T=100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "rIPFOuKAqjzV"
   },
   "outputs": [],
   "source": [
    "residual=df_train[use_feature][n_steps:(n_steps+T)].values-(sigma*pred_train[:T, 0]+mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "2-radzroqjzb"
   },
   "outputs": [],
   "source": [
    "lb,p=sm.stats.diagnostic.acorr_ljungbox(residual, lags=20, boxpierce=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WWvgE9ouqjzf"
   },
   "source": [
    "The Box-Ljung test statistics are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Rn0gmXkDqjzg",
    "outputId": "517efe22-705e-420e-f8ed-e3d4f0180835"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([17145.79470896, 17175.19795798, 17253.24855096, 17314.11952185,\n",
       "       17398.53486084, 17453.94200507, 17458.58977022, 17458.86007284,\n",
       "       17459.12506354, 17487.48212127, 17611.68797122, 17635.65544221,\n",
       "       17637.7658394 , 17637.88988689, 17640.91371593, 17668.61017841,\n",
       "       17707.4052102 , 17728.21403799, 17741.87293566, 17765.9719557 ])"
      ]
     },
     "execution_count": 100,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "D0MmBUaDqjzk"
   },
   "source": [
    "The p-values are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "TTEIIp-Sqjzn",
    "outputId": "15031561-6612-43b6-99c0-dafa4a5c034e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0.])"
      ]
     },
     "execution_count": 101,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "ML_in_Finance-RNNs-Bitcoin.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
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