time_series_analysis.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "time-series-analysis.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/martin-fabbri/colab-notebooks/blob/master/time_series_analysis.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BGW0ggXLwpFw",
        "colab_type": "text"
      },
      "source": [
        "# Time Series Analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tccuiCiUf4ZD",
        "colab_type": "text"
      },
      "source": [
        "## Dependencies"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O8kV8wjMf7GT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "from math import sqrt\n",
        "from statsmodels.tsa.stattools import acf\n",
        "from statsmodels.graphics.tsaplots import plot_acf\n",
        "from statsmodels.tsa.stattools import adfuller\n",
        "from statsmodels.tsa.arima_process import ArmaProcess\n",
        "from statsmodels.tsa.arima_model import ARMA\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l6_i5fSqf83G",
        "colab_type": "text"
      },
      "source": [
        "## Google Diet Search Trends\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-teXkHAxwmzG",
        "colab_type": "code",
        "outputId": "60787f5d-ad8b-4647-af84-ad324a452809",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        }
      },
      "source": [
        "google_diet_search_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/diet_serach_google_trends.csv'\n",
        "\n",
        "diet = pd.read_csv(google_diet_search_url, parse_dates=['month'], index_col=['month'])\n",
        "#diet.index = pd.to_datetime(diet.index)\n",
        "diet.info()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "DatetimeIndex: 192 entries, 2004-01-01 to 2019-12-01\n",
            "Data columns (total 1 columns):\n",
            "diet    192 non-null int64\n",
            "dtypes: int64(1)\n",
            "memory usage: 3.0 KB\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wM3943U9k95O",
        "colab_type": "code",
        "outputId": "57106200-e78c-4297-98ea-86061a81358b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        }
      },
      "source": [
        "diet.plot(grid=True);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Djs5mEAt6UBNwiw1VgSVYNMJ0mqPmrlDUMuPOTZbJXuQi1r06yWjGd4zjfl8mx7hXsedO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\nCfLK3TnnSpBX7s45V4K8cnfOuRL0P3Gx6i1T76n+AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8zx1WQKblyVo",
        "colab_type": "code",
        "outputId": "05946a5e-aa17-4d75-b323-3b0e385f8122",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 527
        }
      },
      "source": [
        "diet2012 = diet[diet.index.year >= 2012]\n",
        "print(diet2012.head())\n",
        "print(diet2012.tail())\n",
        "diet2012.plot(grid=True);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "            diet\n",
            "month           \n",
            "2012-01-01    78\n",
            "2012-02-01    69\n",
            "2012-03-01    69\n",
            "2012-04-01    66\n",
            "2012-05-01    64\n",
            "            diet\n",
            "month           \n",
            "2019-08-01    50\n",
            "2019-09-01    48\n",
            "2019-10-01    46\n",
            "2019-11-01    43\n",
            "2019-12-01    40\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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v7NmPuHCYP/71JJfDkr/+4cs8sMLaMWsjUcnLRycIXiNL8tkbzdjYmO3tPHs+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\nqZVZEbhLP05F5K0Wk5qXK5tTPcyLbW6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CNszs6GiuypotE4knVRHPVcimUB07ThXpwIUQ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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fOQ0RoPzCDdy",
        "colab_type": "text"
      },
      "source": [
        "## Merging Time Series With Different Dates\n",
        "\n",
        "Stock and bond markets in the U.S. are closed on different days. For example, although the bond market is closed on Columbus Day (around Oct 12) and Veterans Day (around Nov 11), the stock market is open on those days. One way to see the dates that the stock market is open and the bond market is closed is to convert both indexes of dates into sets and take the difference in sets.\n",
        "\n",
        "The pandas .join() method is a convenient tool to merge the stock and bond DataFrames on dates when both markets are open."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K61wVJ3IlySZ",
        "colab_type": "code",
        "outputId": "859cbf88-8fe8-4061-f86e-2f1a964d2ff9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        }
      },
      "source": [
        "stocks_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/gspc_sp500_stocks.csv'\n",
        "bonds_url='https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/tnx_us_bonds_us10y.csv'\n",
        "\n",
        "stocks = pd.read_csv(stocks_url, parse_dates=['Date'], index_col=['Date'])\n",
        "bonds = pd.read_csv(bonds_url, parse_dates=['Date'], index_col=['Date'])\n",
        "print(stocks.head())\n",
        "print(bonds.head())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                   Open         High  ...    Adj Close      Volume\n",
            "Date                                  ...                         \n",
            "2010-12-30  1259.439941  1261.089966  ...  1257.880005  1970720000\n",
            "2010-12-31  1256.760010  1259.339966  ...  1257.640015  1799770000\n",
            "2011-01-03  1257.619995  1276.170044  ...  1271.869995  4286670000\n",
            "2011-01-04  1272.949951  1274.119995  ...  1270.199951  4796420000\n",
            "2011-01-05  1268.780029  1277.630005  ...  1276.560059  4764920000\n",
            "\n",
            "[5 rows x 6 columns]\n",
            "             Open   High    Low  Close  Adj Close  Volume\n",
            "Date                                                     \n",
            "2010-12-30  3.384  3.421  3.355  3.369      3.369     0.0\n",
            "2010-12-31  3.324  3.363  3.282  3.305      3.305     0.0\n",
            "2011-01-02    NaN    NaN    NaN    NaN        NaN     NaN\n",
            "2011-01-03  3.377  3.420  3.313  3.342      3.342     0.0\n",
            "2011-01-04  3.338  3.362  3.302  3.346      3.346     0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_2niLym3lyO8",
        "colab_type": "code",
        "outputId": "2e278921-bd1e-4c88-d2cc-29152899760e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 373
        }
      },
      "source": [
        "# Convert the stock index and bond index into sets\n",
        "set_stock_dates = set(stocks.index)\n",
        "set_bond_dates = set(bonds.index)\n",
        "\n",
        "# Take the difference between the sets and print\n",
        "print(set_stock_dates - set_bond_dates)\n",
        "\n",
        "stocks_and_bonds = stocks.join(bonds, how='inner', lsuffix='_stc', rsuffix='_bnd')\n",
        "stocks_and_bonds.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{Timestamp('2016-10-10 00:00:00'), Timestamp('2016-11-11 00:00:00')}\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Open_stc</th>\n",
              "      <th>High_stc</th>\n",
              "      <th>Low_stc</th>\n",
              "      <th>Close_stc</th>\n",
              "      <th>Adj Close_stc</th>\n",
              "      <th>Volume_stc</th>\n",
              "      <th>Open_bnd</th>\n",
              "      <th>High_bnd</th>\n",
              "      <th>Low_bnd</th>\n",
              "      <th>Close_bnd</th>\n",
              "      <th>Adj Close_bnd</th>\n",
              "      <th>Volume_bnd</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2010-12-30</th>\n",
              "      <td>1259.439941</td>\n",
              "      <td>1261.089966</td>\n",
              "      <td>1256.319946</td>\n",
              "      <td>1257.880005</td>\n",
              "      <td>1257.880005</td>\n",
              "      <td>1970720000</td>\n",
              "      <td>3.384</td>\n",
              "      <td>3.421</td>\n",
              "      <td>3.355</td>\n",
              "      <td>3.369</td>\n",
              "      <td>3.369</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2010-12-31</th>\n",
              "      <td>1256.760010</td>\n",
              "      <td>1259.339966</td>\n",
              "      <td>1254.189941</td>\n",
              "      <td>1257.640015</td>\n",
              "      <td>1257.640015</td>\n",
              "      <td>1799770000</td>\n",
              "      <td>3.324</td>\n",
              "      <td>3.363</td>\n",
              "      <td>3.282</td>\n",
              "      <td>3.305</td>\n",
              "      <td>3.305</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-01-03</th>\n",
              "      <td>1257.619995</td>\n",
              "      <td>1276.170044</td>\n",
              "      <td>1257.619995</td>\n",
              "      <td>1271.869995</td>\n",
              "      <td>1271.869995</td>\n",
              "      <td>4286670000</td>\n",
              "      <td>3.377</td>\n",
              "      <td>3.420</td>\n",
              "      <td>3.313</td>\n",
              "      <td>3.342</td>\n",
              "      <td>3.342</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-01-04</th>\n",
              "      <td>1272.949951</td>\n",
              "      <td>1274.119995</td>\n",
              "      <td>1262.660034</td>\n",
              "      <td>1270.199951</td>\n",
              "      <td>1270.199951</td>\n",
              "      <td>4796420000</td>\n",
              "      <td>3.338</td>\n",
              "      <td>3.362</td>\n",
              "      <td>3.302</td>\n",
              "      <td>3.346</td>\n",
              "      <td>3.346</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-01-05</th>\n",
              "      <td>1268.780029</td>\n",
              "      <td>1277.630005</td>\n",
              "      <td>1265.359985</td>\n",
              "      <td>1276.560059</td>\n",
              "      <td>1276.560059</td>\n",
              "      <td>4764920000</td>\n",
              "      <td>3.381</td>\n",
              "      <td>3.497</td>\n",
              "      <td>3.379</td>\n",
              "      <td>3.483</td>\n",
              "      <td>3.483</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "               Open_stc     High_stc  ...  Adj Close_bnd  Volume_bnd\n",
              "Date                                  ...                           \n",
              "2010-12-30  1259.439941  1261.089966  ...          3.369         0.0\n",
              "2010-12-31  1256.760010  1259.339966  ...          3.305         0.0\n",
              "2011-01-03  1257.619995  1276.170044  ...          3.342         0.0\n",
              "2011-01-04  1272.949951  1274.119995  ...          3.346         0.0\n",
              "2011-01-05  1268.780029  1277.630005  ...          3.483         0.0\n",
              "\n",
              "[5 rows x 12 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wCUA-j85TXEU",
        "colab_type": "text"
      },
      "source": [
        "## Correlation of Stocks and Bonds"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pfhm5VfaCReA",
        "colab_type": "code",
        "outputId": "4d1339dc-409b-41e1-8683-47d083222834",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        }
      },
      "source": [
        "returns = stocks_and_bonds.pct_change()\n",
        "print(returns.head())\n",
        "correlation = returns['Close_stc'].corr(returns['Close_bnd'])\n",
        "print(correlation)\n",
        "plt.scatter(returns['Close_stc'], returns['Close_bnd']);\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "            Open_stc  High_stc   Low_stc  ...  Close_bnd  Adj Close_bnd  Volume_bnd\n",
            "Date                                      ...                                      \n",
            "2010-12-30       NaN       NaN       NaN  ...        NaN            NaN         NaN\n",
            "2010-12-31 -0.002128 -0.001388 -0.001695  ...  -0.018997      -0.018997         NaN\n",
            "2011-01-03  0.000684  0.013364  0.002735  ...   0.011195       0.011195         NaN\n",
            "2011-01-04  0.012190 -0.001606  0.004008  ...   0.001197       0.001197         NaN\n",
            "2011-01-05 -0.003276  0.002755  0.002138  ...   0.040944       0.040944         NaN\n",
            "\n",
            "[5 rows x 12 columns]\n",
            "0.4381423924113941\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ODVFLiZrpETbjyCmTqUism9ObWUB+3wv7iuEwn2FeMpGyioGAWk7YFNConcm0ctv4c9tQ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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EqdlvB07sxrq",
        "colab_type": "text"
      },
      "source": [
        "## Flying Saucers Aren't Correlated to Flying Markets\n",
        "\n",
        "Two trending series may show a strong correlation even if they are completely unrelated. This is referred to as \"spurious correlation\". That's why when you look at the correlation of say, two stocks, you should look at the correlation of their returns and not their levels.\n",
        "\n",
        "To illustrate this point, calculate the correlation between the levels of the stock market and the annual sightings of UFOs. Both of those time series have trended up over the last several decades, and the correlation of their levels is very high. Then calculate the correlation of their percent changes. This will be close to zero, since there is no relationship between those two series."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tFuMfLQ3sxY4",
        "colab_type": "code",
        "outputId": "9d80bcc1-a346-4263-fe0b-10c9a50dfcb4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 763
        }
      },
      "source": [
        "dji_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/financial-time-series/dow_jones_1990_2019.csv'\n",
        "ufo_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/ufo_national_reporting.csv'\n",
        "\n",
        "dji = pd.read_csv(dji_url, parse_dates=['month'], index_col=['month'])\n",
        "ufo = pd.read_csv(ufo_url, parse_dates=['month'], index_col=['month'])\n",
        "\n",
        "print(dji.head())\n",
        "print(ufo.head())\n",
        "\n",
        "dji = dji.resample('Y').sum()\n",
        "ufo = ufo.resample('Y').sum()\n",
        "\n",
        "print(dji.head())\n",
        "print(ufo.head())\n",
        "\n",
        "levels = dji.join(ufo, how='inner')\n",
        "print(levels.head())\n",
        "print(levels.tail())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                  close\n",
            "month                  \n",
            "1990-01-01  2590.540039\n",
            "1990-02-01  2627.250000\n",
            "1990-03-01  2707.209961\n",
            "1990-04-01  2656.760010\n",
            "1990-05-01  2876.659912\n",
            "            count\n",
            "month            \n",
            "2019-12-01    452\n",
            "2019-11-01    679\n",
            "2019-10-01    705\n",
            "2019-09-01    644\n",
            "2019-08-01    465\n",
            "                   close\n",
            "month                   \n",
            "1990-12-31  31946.789793\n",
            "1991-12-31  35572.350343\n",
            "1992-12-31  39556.609862\n",
            "1993-12-31  42451.450440\n",
            "1994-12-31  45514.260008\n",
            "            count\n",
            "month            \n",
            "1990-12-31      6\n",
            "1991-12-31    117\n",
            "1992-12-31    129\n",
            "1993-12-31    145\n",
            "1994-12-31    191\n",
            "                   close  count\n",
            "month                          \n",
            "1990-12-31  31946.789793      6\n",
            "1991-12-31  35572.350343    117\n",
            "1992-12-31  39556.609862    129\n",
            "1993-12-31  42451.450440    145\n",
            "1994-12-31  45514.260008    191\n",
            "                   close  count\n",
            "month                          \n",
            "2015-12-31  209855.55373   6909\n",
            "2016-12-31  216328.59179   5686\n",
            "2017-12-31  263251.46092   5043\n",
            "2018-12-31  299952.10158   3395\n",
            "2019-12-31  318596.41994   5791\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5tPxZ9KasxWd",
        "colab_type": "code",
        "outputId": "02486622-cf38-4068-fd76-d68382fd07a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "correlation1 = levels['close'].corr(levels['count'])\n",
        "print(\"Correlation of levels: \", correlation1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Correlation of levels:  0.6691135250162759\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EDZYAtkrsxTg",
        "colab_type": "code",
        "outputId": "20ccf9b8-2c32-456d-831b-596ce943ecd4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "changes = levels.pct_change()\n",
        "correlation2 = changes['close'].corr(changes['count'])\n",
        "print(\"Correlation of levels: \", correlation2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Correlation of levels:  0.0420344334388898\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5y6K2b8gOHQw",
        "colab_type": "text"
      },
      "source": [
        "## Autocorrelation\n",
        "\n",
        "One puzzling anomaly with stocks is that investors tend to overreact to news. Following large jumps, either up or down, stock prices tend to reverse. This is described as mean reversion in stock prices: prices tend to bounce back, or revert, towards previous levels after large moves, which are observed over time horizons of about a week. A more mathematical way to describe mean reversion is to say that stock returns are negatively autocorrelated.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9jR0PxQnsxQO",
        "colab_type": "code",
        "outputId": "c11387d1-c34f-4007-d80e-af5ad148bcb7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "msft_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/financial-time-series/msft_2013_2019.csv'\n",
        "msft = pd.read_csv(msft_url, parse_dates=['date'], index_col=['date'])\n",
        "msft = msft.resample('W').last()\n",
        "returns = msft.pct_change()\n",
        "autocorrelation = returns['adj_close'].autocorr()\n",
        "print('The autocorrelation of weekly returns is %4.2f' %(autocorrelation))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The autocorrelation of weekly returns is -0.18\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2EO1JRjKiwIV",
        "colab_type": "text"
      },
      "source": [
        "## Are Interest Rates Autocorrelated?\n",
        "\n",
        "When you look at daily changes in interest rates, the autocorrelation is close to zero. However, if you resample the data and look at annual changes, the autocorrelation is negative. This implies that while short term changes in interest rates may be uncorrelated, long term changes in interest rates are negatively autocorrelated. A daily move up or down in interest rates is unlikely to tell you anything about interest rates tomorrow, but a move in interest rates over a year can tell you something about where interest rates are going over the next year. And this makes some economic sense: over long horizons, when interest rates go up, the economy tends to slow down, which consequently causes interest rates to fall, and vice versa."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pbsf2Q0yivkp",
        "colab_type": "code",
        "outputId": "68be1c95-91d3-4c44-be7c-ad4d412b5377",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        }
      },
      "source": [
        "bonds_url='https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/tnx_us_bonds_us10y.csv'\n",
        "bonds = pd.read_csv(bonds_url, parse_dates=['Date'], index_col=['Date'])\n",
        "\n",
        "daily_rates = bonds[['Adj Close']]\n",
        "daily_rates = daily_rates.dropna()\n",
        "daily_rates.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Adj Close</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2010-12-30</th>\n",
              "      <td>3.369</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2010-12-31</th>\n",
              "      <td>3.305</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-01-03</th>\n",
              "      <td>3.342</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-01-04</th>\n",
              "      <td>3.346</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-01-05</th>\n",
              "      <td>3.483</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Adj Close\n",
              "Date                 \n",
              "2010-12-30      3.369\n",
              "2010-12-31      3.305\n",
              "2011-01-03      3.342\n",
              "2011-01-04      3.346\n",
              "2011-01-05      3.483"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7pvSraCRCRmm",
        "colab_type": "code",
        "outputId": "3e6a6a8d-bd38-4102-80ab-ebac87403cb4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "daily_diff = daily_rates.diff()\n",
        "autocorrelation_daily = daily_diff['Adj Close'].autocorr()\n",
        "print('The autocorrelation of daily interest rate changes is %4.2f' %(autocorrelation_daily))\n",
        "yearly_rates = daily_rates.resample('A').last()\n",
        "yearly_diff = yearly_rates.diff()\n",
        "autocorrelation_yearly = yearly_diff['Adj Close'].autocorr()\n",
        "print(\"The autocorrelation of annual interest rate changes is %4.2f\" %(autocorrelation_yearly))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The autocorrelation of daily interest rate changes is -0.03\n",
            "The autocorrelation of annual interest rate changes is -0.37\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sxc-x2fNnfaf",
        "colab_type": "text"
      },
      "source": [
        "## Taxing Company: Compute the ACF"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q5W7l2bLCRj7",
        "colab_type": "code",
        "outputId": "d51ee814-ef40-49df-e5b1-38b14f0793aa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "hrb_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/financial-time-series/HRB.csv'\n",
        "hrb = pd.read_csv(hrb_url, parse_dates=['Quarter'], index_col=['Quarter'])\n",
        "acf_array = acf(hrb, fft=True)\n",
        "plot_acf(acf_array, alpha=1)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gXQbcHBHvSqY/DhARf5Rq82DS5nuSJgMHga4YpvOzz5sXl//uHeOqaeuTWwFYcPGCcT2/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\nWUH8fz/zBE482vjDAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ubrXjjAbwoTw",
        "colab_type": "text"
      },
      "source": [
        "## Are We Confident This Stock is Mean Reverting?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y_k-rYYTsTFz",
        "colab_type": "code",
        "outputId": "1e6c6409-f3ad-4e2d-f873-1708c2733f3f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        }
      },
      "source": [
        "msft_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/financial-time-series/msft_2013_2019.csv'\n",
        "msft = pd.read_csv(msft_url, parse_dates=['date'], index_col=['date'])\n",
        "msft = msft.resample('W').last()\n",
        "returns = msft.pct_change()\n",
        "autocorrelation = returns['adj_close'].autocorr()\n",
        "print(\"The autocorrelation of weekly MSFT returns is %4.2f\" %(autocorrelation))\n",
        "nobs = len(returns)\n",
        "conf = 1.96/sqrt(nobs)\n",
        "print(\"The approximate confidence interval is +/- %4.2f\" %(conf))\n",
        "plot_acf(returns['adj_close'], alpha=0.05, lags=20);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The autocorrelation of weekly MSFT returns is -0.18\n",
            "The approximate confidence interval is +/- 0.10\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AJB8EnjLLqdcPNqqqktSwL5zkJOBpVfXqJGvnG19Vm4BNAL1eb+jXkSQ9vnmDoKrOmOtc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\nBy2pQiGH/UVNAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FFTXwTTh2A_8",
        "colab_type": "text"
      },
      "source": [
        "## Can't Forecast White Noise\n",
        "\n",
        "A white noise time series is simply a sequence of uncorrelated random variables that are identically distributed. Stock returns are often modeled as white noise. Unfortunately, for white noise, we cannot forecast future observations based on the past - autocorrelations at all lags are zero.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2FQZLZ_isTYo",
        "colab_type": "code",
        "outputId": "dd2dd340-6803-4568-a713-875c2814af83",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 546
        }
      },
      "source": [
        "returns = np.random.normal(loc=0.02, scale=0.05, size=1000)\n",
        "\n",
        "mean = np.mean(returns)\n",
        "std = np.std(returns)\n",
        "\n",
        "print(\"The mean is %5.3f and the standard deviation is %5.3f\" %(mean,std))\n",
        "\n",
        "plt.plot(returns)\n",
        "plot_acf(returns, lags=20);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The mean is 0.019 and the standard deviation is 0.049\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7q3Ok9catGhK5hMra0I186rtjFJS/+p8z8O6C+qy9RXjvs1C/bbeX+1GmzlCB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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lNP7P5RBpXtv",
        "colab_type": "text"
      },
      "source": [
        "## Evaluate Random Walk\n",
        "\n",
        "Whereas stock returns are often modeled as white noise, stock prices closely follow a random walk. In other words, today's price is yesterday's price plus some random noise."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PHuzM5P5sTVR",
        "colab_type": "code",
        "outputId": "27f37a33-39f1-4d19-9b9d-d39a5d0bc132",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "steps = np.random.normal(loc=0, scale=1, size=500)\n",
        "steps[0] = 0\n",
        "P = 100 + np.cumsum(steps)\n",
        "plt.plot(P);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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k/wUZmTq7FA7pDUbwkVPb0CwnqP3f2n14/69ez7t7puS/WfV2IwY8QfhDUlbY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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4lutP8AgsTRg",
        "colab_type": "code",
        "outputId": "7b00ab79-4a6d-482e-b187-7d7a0704cee6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "steps = np.random.normal(loc=0.001, scale=0.01, size=500) + 1\n",
        "steps[0] = 1\n",
        "P = 100 * np.cumprod(steps)\n",
        "plt.plot(P)\n",
        "plt.title('Simulated random walk with drift');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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WUsp/gj64e096fNZxmT7bbjtvHu/ddobnlvk7f9lG5xAmt954uIbj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\nV0qpIPT/ASe9MQzVeoC8AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jQkZxtGfv9I1",
        "colab_type": "text"
      },
      "source": [
        "## Are Stock Prices a Random Walk?\n",
        "\n",
        "With the ADF test, the \"null hypothesis\" (the hypothesis that we either reject or fail to reject) is that the series follows a random walk. Therefore, a low p-value (say less than 5%) means we can reject the null hypothesis that the series is a random walk."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fgxFN0PvsTOb",
        "colab_type": "code",
        "outputId": "45a01aec-dcba-4c94-b3bb-ed8dd80f88a8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        }
      },
      "source": [
        "amzn_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/financial-time-series/AMZN.csv'\n",
        "AMZN = pd.read_csv(amzn_url, parse_dates=['Date'], index_col=['Date'])\n",
        "results = adfuller(AMZN['Adj Close'])\n",
        "print(results)\n",
        "print('The p-value of the test on prices is: ' + str(results[1]))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(4.02516852577074, 1.0, 33, 5054, {'1%': -3.4316445438146865, '5%': -2.862112049726916, '10%': -2.5670745025321304}, 30308.64216426981)\n",
            "The p-value of the test on prices is: 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6bF_cXawsTLt",
        "colab_type": "code",
        "outputId": "d68f8a89-b0d3-4a5d-faf0-b4e9123dd782",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        }
      },
      "source": [
        "AMZN.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Adj Close</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1997-05-15</th>\n",
              "      <td>1.958333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-16</th>\n",
              "      <td>1.729167</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-19</th>\n",
              "      <td>1.708333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-20</th>\n",
              "      <td>1.635417</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-21</th>\n",
              "      <td>1.427083</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Adj Close\n",
              "Date                 \n",
              "1997-05-15   1.958333\n",
              "1997-05-16   1.729167\n",
              "1997-05-19   1.708333\n",
              "1997-05-20   1.635417\n",
              "1997-05-21   1.427083"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0Yw8FMRJ5oU0",
        "colab_type": "text"
      },
      "source": [
        "## How About Stock Returns?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k7hzlKfC5nh7",
        "colab_type": "code",
        "outputId": "bed4be38-d665-4a78-8955-b135332052bf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        }
      },
      "source": [
        "AMZN_ret = AMZN.pct_change()\n",
        "\n",
        "AMZN_ret = AMZN_ret.dropna()\n",
        "results = adfuller(AMZN_ret['Adj Close'])\n",
        "print(results)\n",
        "print('The p-value of the test on returns is: ' + str(results[1]))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(-12.053453021869718, 2.565589808347808e-22, 33, 5053, {'1%': -3.431644800138127, '5%': -2.86211216296977, '10%': -2.567074562815631}, -18483.377508750207)\n",
            "The p-value of the test on returns is: 2.565589808347808e-22\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JEuOufIM5nec",
        "colab_type": "code",
        "outputId": "b8904e4c-1ca9-411d-aa56-dbdfa6343bcd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        }
      },
      "source": [
        "AMZN.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Adj Close</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1997-05-15</th>\n",
              "      <td>1.958333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-16</th>\n",
              "      <td>1.729167</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-19</th>\n",
              "      <td>1.708333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-20</th>\n",
              "      <td>1.635417</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1997-05-21</th>\n",
              "      <td>1.427083</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Adj Close\n",
              "Date                 \n",
              "1997-05-15   1.958333\n",
              "1997-05-16   1.729167\n",
              "1997-05-19   1.708333\n",
              "1997-05-20   1.635417\n",
              "1997-05-21   1.427083"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9yjTAz0GF0xp",
        "colab_type": "text"
      },
      "source": [
        "## Seasonal Adjustment During Tax Season\n",
        "\n",
        "Many time series exhibit strong seasonal behavior. The procedure for removing the seasonal component of a time series is called seasonal adjustment. For example, most economic data published by the government is seasonally adjusted."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cG9egv0zHHMy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "hrb_url = 'https://raw.githubusercontent.com/martin-fabbri/colab-notebooks/master/data/financial-time-series/HRB.csv'\n",
        "HRB = pd.read_csv(hrb_url, parse_dates=['Quarter'], index_col=['Quarter'])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DpxlK8f85nbX",
        "colab_type": "code",
        "outputId": "632fdf8b-a3b1-4dc2-e253-9c3ac3ca93eb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 494
        }
      },
      "source": [
        "HRBsa = HRB.diff(4)\n",
        "print(HRBsa.head(10))\n",
        "HRBsa = HRBsa.dropna()\n",
        "plot_acf(HRBsa);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "            Earnings\n",
            "Quarter             \n",
            "2007-01-01       NaN\n",
            "2007-04-01       NaN\n",
            "2007-07-01       NaN\n",
            "2007-10-01       NaN\n",
            "2008-01-01      0.02\n",
            "2008-04-01     -0.04\n",
            "2008-07-01     -0.05\n",
            "2008-10-01      0.26\n",
            "2009-01-01     -0.05\n",
            "2009-04-01      0.02\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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wa/hQvxg6OsQ155/GrA3f5Ih//xG/+7qlPoqztpdL4EtaIekxSb2Srq4z/oOSNkh6WNLd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\nbAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bEbvTXeqnKL8",
        "colab_type": "text"
      },
      "source": [
        "## Simulate AR(1) Time Series\n",
        "\n",
        "You will simulate and plot a few AR(1) time series, each with a different parameter, ϕ, using the arima_process module in statsmodels. In this exercise, you will look at an AR(1) model with a large positive ϕ and a large negative ϕ, but feel free to play around with your own parameters.\n",
        "\n",
        "There are a few conventions when using the arima_process module that require some explanation. First, these routines were made very generally to handle both AR and MA models. We will cover MA models next, so for now, just ignore the MA part. Second, when inputting the coefficients, you must include the zero-lag coefficient of 1, and the sign of the other coefficients is opposite what we have been using (to be consistent with the time series literature in signal processing). For example, for an AR(1) process with ϕ=0.9, the array representing the AR parameters would be ar = np.array([1, -0.9])"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hebqT8LR5nYR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "09a483a7-f788-462c-9ee3-62ac5ed57bcc"
      },
      "source": [
        "# Plot 1: AR parameter = +0.9\n",
        "plt.subplot(2, 1, 1)\n",
        "ar1 = np.array([1, -0.9])\n",
        "ma1 = np.array([1])\n",
        "\n",
        "AR_object1 = ArmaProcess(ar1, ma1)\n",
        "simulated_data_1 = AR_object1.generate_sample(nsample=1000)\n",
        "plt.plot(simulated_data_1);\n",
        "\n",
        "plt.subplot(2, 1, 2)\n",
        "ar2 = np.array([1, 0.9])\n",
        "ma2 = np.array([1])\n",
        "AR_object2 = ArmaProcess(ar2, ma2)\n",
        "simulated_data_2 = AR_object2.generate_sample(nsample=1000)\n",
        "plt.plot(simulated_data_2);\n",
        "\n",
        "# plt.subplot(2,2,1)\n",
        "ar3 = np.array([1, -0.3])\n",
        "ma3 = np.array([1])\n",
        "AR_object3 = ArmaProcess(ar3, ma3)\n",
        "simulated_data_3 = AR_object3.generate_sample(nsample=1000)\n",
        "# plt.plot(simulated_data_3);\n"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0zUiRFjJg/CNClhnrjHyJ0eaW3VlW04iF24tVtUJeHv135QE89+tOAOY725Tn/npdIfre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\norsnYck9k5WHCCEeU3r+mON6h48nz83QDhkmhIAQghX3nip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            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Gxjqzu3tEqS",
        "colab_type": "text"
      },
      "source": [
        "## Compare the ACF for Several AR Time Series\n",
        "The autocorrelation function decays exponentially for an AR time series at a rate of the AR parameter. For example, if the AR parameter, ϕ=+0.9, the first-lag autocorrelation will be 0.9, the second-lag will be (0.9)^2=0.81, the third-lag will be (0.9)^3=0.729, etc. A smaller AR parameter will have a steeper decay, and for a negative AR parameter, say -0.9, the decay will flip signs, so the first-lag autocorrelation will be -0.9, the second-lag will be (−0.9)^2=0.81, the third-lag will be (−0.9)^3=−0.729, etc.\n",
        "\n",
        "The object simulated_data_1 is the simulated time series with an AR parameter of +0.9, simulated_data_2 is for an AR parameter of -0.9, and simulated_data_3 is for an AR parameter of 0.3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PkdI1cyS5nV1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 809
        },
        "outputId": "99d33ac9-6a29-4b0a-d6c5-a238a84d96b3"
      },
      "source": [
        "# Plot 1: AR parameter = +0.9\n",
        "plot_acf(simulated_data_1, alpha=1, lags=20);\n",
        "plot_acf(simulated_data_2, alpha=1, lags=20);\n",
        "plot_acf(simulated_data_3, alpha=1, lags=20);"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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L81kT4CAwM8tdXn0TQzxqyMysCeQxjccQXxGYmRWcg8DMrOAcBGZmBVeTIJC0WNIWSdsk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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GPgVcFBH+ok4zswYoG+gRcRy4DLgd2A1sjoidkq6SdFE22weB+cA/SdohqW+KlzMzszrJ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\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yHJplU8t1DYH",
        "colab_type": "text"
      },
      "source": [
        "## Estimating an AR Model\n",
        "You will estimate the AR(1) parameter, ϕ, of one of the simulated series that you generated in the earlier exercise. Since the parameters are known for a simulated series, it is a good way to understand the estimation routines before applying it to real data.\n",
        "\n",
        "For simulated_data_1 with a true ϕ of 0.9, you will print out the estimate of ϕ. In addition, you will also print out the entire output that is produced when you fit a time series, so you can get an idea of what other tests and summary statistics are available in statsmodels."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mSjJ03aY5nSP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 425
        },
        "outputId": "4d8acdb7-a174-446d-9768-7872fc22f2a9"
      },
      "source": [
        "# Fit an AR(1) model to the first simulated data\n",
        "mod = ARMA(simulated_data_1, order=(1,0))\n",
        "res = mod.fit()\n",
        "print(res.summary())\n",
        "print('---')\n",
        "print('When the true phi=0.9, the estimate of phi (and the constant) are:')\n",
        "print(res.params)\n"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                              ARMA Model Results                              \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                 1000\n",
            "Model:                     ARMA(1, 0)   Log Likelihood               -1439.282\n",
            "Method:                       css-mle   S.D. of innovations              1.020\n",
            "Date:                Wed, 01 Jan 2020   AIC                           2884.564\n",
            "Time:                        06:49:03   BIC                           2899.288\n",
            "Sample:                             0   HQIC                          2890.160\n",
            "                                                                              \n",
            "==============================================================================\n",
            "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -0.0758      0.343     -0.221      0.825      -0.749       0.597\n",
            "ar.L1.y        0.9070      0.013     68.335      0.000       0.881       0.933\n",
            "                                    Roots                                    \n",
            "=============================================================================\n",
            "                  Real          Imaginary           Modulus         Frequency\n",
            "-----------------------------------------------------------------------------\n",
            "AR.1            1.1025           +0.0000j            1.1025            0.0000\n",
            "-----------------------------------------------------------------------------\n",
            "---\n",
            "When the true phi=0.9, the estimate of phi (and the constant) are:\n",
            "[-0.07577072  0.90700747]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KVge2kIZ3xA5",
        "colab_type": "text"
      },
      "source": [
        "## Forecasting with an AR Model\n",
        "\n",
        "In addition to estimating the parameters of a model that you did in the last exercise, you can also do forecasting, both in-sample and out-of-sample using statsmodels. The in-sample is a forecast of the next data point using the data up to that point, and the out-of-sample forecasts any number of data points in the future. These forecasts can be made using either the predict() method if you want the forecasts in the form of a series of data, or using the plot_predict() method if you want a plot of the forecasted data. You supply the starting point for forecasting and the ending point, which can be any number of data points after the data set ends.\n",
        "\n",
        "For the simulated series simulated_data_1 with ϕ=0.9, you will plot in-sample and out-of-sample forecasts."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XqFjUJQZ5nPE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "20a866cc-036a-45cc-e367-84c640c3ecd9"
      },
      "source": [
        "mod = ARMA(simulated_data_1, order=(1,0))\n",
        "res = mod.fit()\n",
        "res.plot_predict(start=990, end=1010);"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0i7KdiYF/hqDWZ3TVH2gxcc95Xfj1UD5ft5Q1+8sLHEsuu7FD9/nv09l3rIRn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\nYSTxCyFECyOJXwghWpj/B+MVZD63WSaPAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jTjf0kbO9AwS",
        "colab_type": "text"
      },
      "source": [
        "## Let's Forecast Interest Rates\n",
        "You will now use the forecasting techniques you learned in the last exercise and apply it to real data rather than simulated data. You will revisit a dataset from the first chapter: the annual data of 10-year interest rates going back 56 years, which is in a Series called interest_rate_data. Being able to forecast interest rates is of enormous importance, not only for bond investors but also for individuals like new homeowners who must decide between fixed and floating rate mortgages.\n",
        "\n",
        "You saw in the first chapter that there is some mean reversion in interest rates over long horizons. In other words, when interest rates are high, they tend to drop and when they are low, they tend to rise over time. Currently they are below long-term rates, so they are expected to rise, but an AR model attempts to quantify how much they are expected to rise."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YUqy9Cua9BdM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7BbG6MUu9Ba8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "78iimG0M9BXV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DIKCoGJJ9BUd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d8jGAh1Z9BRl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}