Auto_ARIMA.ipynb

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    "language_info": {
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        "name": "ipython",
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      "pygments_lexer": "ipython3",
      "version": "3.6.7"
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    "colab": {
      "name": "Auto ARIMA.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/RegaipKURT/Machine-Learning-Python/blob/master/Auto_ARIMA.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uzlwXQEmEd98",
        "colab_type": "text"
      },
      "source": [
        "### Packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ijO07ssIEntd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip3 install arch yfinance pmdarima"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_9qBqUaCEd9-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        },
        "outputId": "f2e4b305-46cd-4f0e-909b-00a1a45add2b"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import scipy\n",
        "import statsmodels.api as sm\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import sklearn\n",
        "from statsmodels.tsa.arima_model import ARIMA\n",
        "from arch import arch_model\n",
        "import seaborn as sns\n",
        "import yfinance\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "sns.set()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LB1RUHpTEd-F",
        "colab_type": "text"
      },
      "source": [
        "### Loading the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mxl9qvYXEd-G",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "909f0b2c-90f7-46d2-8b76-16710653a061"
      },
      "source": [
        "raw_data = yfinance.download (tickers = \"^GSPC ^FTSE ^N225 ^GDAXI\", start = \"1994-01-07\", end = \"2020-03-31\", \n",
        "                              interval = \"1d\", group_by = 'ticker', auto_adjust = True, treads = True)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[*********************100%***********************]  4 of 4 completed\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nN_Ul-EeEd-M",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df_comp = raw_data.copy()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4oMLzUP3Ed-Q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df_comp['spx'] = df_comp['^GSPC'].Close[:]\n",
        "df_comp['dax'] = df_comp['^GDAXI'].Close[:]\n",
        "df_comp['ftse'] = df_comp['^FTSE'].Close[:]\n",
        "df_comp['nikkei'] = df_comp['^N225'].Close[:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "qBj7IKa4Ed-U",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df_comp = df_comp.iloc[1:]\n",
        "del df_comp['^N225']\n",
        "del df_comp['^GSPC']\n",
        "del df_comp['^GDAXI']\n",
        "del df_comp['^FTSE']\n",
        "df_comp=df_comp.asfreq('b')\n",
        "df_comp=df_comp.fillna(method='ffill')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pBwHEQ6aEd-Y",
        "colab_type": "text"
      },
      "source": [
        "### Creating Returns"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5zq5DYz_Ed-Z",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df_comp['ret_spx'] = df_comp.spx.pct_change(1)*100\n",
        "df_comp['ret_ftse'] = df_comp.ftse.pct_change(1)*100\n",
        "df_comp['ret_dax'] = df_comp.dax.pct_change(1)*100\n",
        "df_comp['ret_nikkei'] = df_comp.nikkei.pct_change(1)*100"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VbCr95XOEd-e",
        "colab_type": "text"
      },
      "source": [
        "### Splitting the Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rdN5XxpvEd-f",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "size = int(len(df_comp)*0.8)\n",
        "df, df_test = df_comp.iloc[:size], df_comp.iloc[size:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dbN_MSgfEd-j",
        "colab_type": "text"
      },
      "source": [
        "### Fitting a Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XDDqduy7Ed-j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from pmdarima.arima import auto_arima"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AklvFnfCEd-n",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_auto = auto_arima(df.ret_ftse[1:])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G1JKiN3zEd-s",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "8e93e8ab-760e-4ce8-a27a-7c167e3d0dd9"
      },
      "source": [
        "model_auto"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "ARIMA(maxiter=50, method='lbfgs', order=(3, 0, 5), out_of_sample_size=0,\n",
              "      scoring='mse', scoring_args=None, seasonal_order=(0, 0, 0, 0),\n",
              "      start_params=None, suppress_warnings=False, trend=None,\n",
              "      with_intercept=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w3vpJIs3Ed-x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 570
        },
        "outputId": "86801b10-55a3-4965-ecc4-45d3add01c27"
      },
      "source": [
        "model_auto.summary()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>Statespace Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>   <td>5472</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>           <td>SARIMAX(3, 0, 5)</td> <th>  Log Likelihood     </th> <td>-8458.667</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>            <td>Wed, 01 Apr 2020</td> <th>  AIC                </th> <td>16937.334</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                <td>23:50:27</td>     <th>  BIC                </th> <td>17003.408</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>                  <td>0</td>        <th>  HQIC               </th> <td>16960.386</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                      <td> - 5472</td>     <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>        <td>opg</td>       <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>intercept</th> <td>    0.0449</td> <td>    0.033</td> <td>    1.348</td> <td> 0.178</td> <td>   -0.020</td> <td>    0.110</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1</th>     <td>   -0.1537</td> <td>    0.076</td> <td>   -2.020</td> <td> 0.043</td> <td>   -0.303</td> <td>   -0.005</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2</th>     <td>   -0.8716</td> <td>    0.019</td> <td>  -45.778</td> <td> 0.000</td> <td>   -0.909</td> <td>   -0.834</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3</th>     <td>   -0.3082</td> <td>    0.070</td> <td>   -4.391</td> <td> 0.000</td> <td>   -0.446</td> <td>   -0.171</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1</th>     <td>    0.1294</td> <td>    0.076</td> <td>    1.695</td> <td> 0.090</td> <td>   -0.020</td> <td>    0.279</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2</th>     <td>    0.8198</td> <td>    0.022</td> <td>   37.409</td> <td> 0.000</td> <td>    0.777</td> <td>    0.863</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3</th>     <td>    0.2021</td> <td>    0.069</td> <td>    2.921</td> <td> 0.003</td> <td>    0.066</td> <td>    0.338</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L4</th>     <td>   -0.0101</td> <td>    0.009</td> <td>   -1.165</td> <td> 0.244</td> <td>   -0.027</td> <td>    0.007</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L5</th>     <td>   -0.1055</td> <td>    0.008</td> <td>  -13.079</td> <td> 0.000</td> <td>   -0.121</td> <td>   -0.090</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>sigma2</th>    <td>    1.2890</td> <td>    0.013</td> <td>   95.996</td> <td> 0.000</td> <td>    1.263</td> <td>    1.315</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Ljung-Box (Q):</th>          <td>75.70</td> <th>  Jarque-Bera (JB):  </th> <td>7360.23</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Q):</th>                <td>0.00</td>  <th>  Prob(JB):          </th>  <td>0.00</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Heteroskedasticity (H):</th> <td>1.80</td>  <th>  Skew:              </th>  <td>-0.16</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(H) (two-sided):</th>    <td>0.00</td>  <th>  Kurtosis:          </th>  <td>8.67</td>  \n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                           Statespace Model Results                           \n",
              "==============================================================================\n",
              "Dep. Variable:                      y   No. Observations:                 5472\n",
              "Model:               SARIMAX(3, 0, 5)   Log Likelihood               -8458.667\n",
              "Date:                Wed, 01 Apr 2020   AIC                          16937.334\n",
              "Time:                        23:50:27   BIC                          17003.408\n",
              "Sample:                             0   HQIC                         16960.386\n",
              "                               - 5472                                         \n",
              "Covariance Type:                  opg                                         \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "intercept      0.0449      0.033      1.348      0.178      -0.020       0.110\n",
              "ar.L1         -0.1537      0.076     -2.020      0.043      -0.303      -0.005\n",
              "ar.L2         -0.8716      0.019    -45.778      0.000      -0.909      -0.834\n",
              "ar.L3         -0.3082      0.070     -4.391      0.000      -0.446      -0.171\n",
              "ma.L1          0.1294      0.076      1.695      0.090      -0.020       0.279\n",
              "ma.L2          0.8198      0.022     37.409      0.000       0.777       0.863\n",
              "ma.L3          0.2021      0.069      2.921      0.003       0.066       0.338\n",
              "ma.L4         -0.0101      0.009     -1.165      0.244      -0.027       0.007\n",
              "ma.L5         -0.1055      0.008    -13.079      0.000      -0.121      -0.090\n",
              "sigma2         1.2890      0.013     95.996      0.000       1.263       1.315\n",
              "===================================================================================\n",
              "Ljung-Box (Q):                       75.70   Jarque-Bera (JB):              7360.23\n",
              "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
              "Heteroskedasticity (H):               1.80   Skew:                            -0.16\n",
              "Prob(H) (two-sided):                  0.00   Kurtosis:                         8.67\n",
              "===================================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iRDs5jYAEd-1",
        "colab_type": "text"
      },
      "source": [
        "### Important Arguments"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "6cGobbjPEd-2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_auto = auto_arima(df_comp.ret_ftse[1:], exogenous = df_comp[['ret_spx', 'ret_dax', 'ret_nikkei']][1:], m = 5,\n",
        "                       max_order = None, max_p = 7, max_q = 7, max_d = 2, max_P = 4, max_Q = 4, max_D = 2,\n",
        "                       maxiter = 50, alpha = 0.05, n_jobs = -1, trend = 'ct', information_criterion = 'oob',\n",
        "                       out_of_sample = int(len(df_comp)*0.2))\n",
        "\n",
        "# exogenous -> outside factors (e.g other time series)\n",
        "# m -> seasonal cycle length\n",
        "# max_order -> maximum amount of variables to be used in the regression (p + q)\n",
        "# max_p -> maximum AR components\n",
        "# max_q -> maximum MA components\n",
        "# max_d -> maximum Integrations\n",
        "# maxiter -> maximum iterations we're giving the model to converge the coefficients (becomes harder as the order increases)\n",
        "# alpha -> level of significance, default is 5%, which we should be using most of the time\n",
        "# n_jobs -> how many models to fit at a time (-1 indicates \"as many as possible\")\n",
        "# trend -> \"ct\" usually\n",
        "# information_criterion -> 'aic', 'aicc', 'bic', 'hqic', 'oob' \n",
        "#        (Akaike Information Criterion, Corrected Akaike Information Criterion,\n",
        "#        Bayesian Information Criterion, Hannan-Quinn Information Criterion, or\n",
        "#        \"out of bag\"--for validation scoring--respectively)\n",
        "# out_of_smaple -> validates the model selection (pass the entire dataset, and set 20% to be the out_of_sample_size)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QScSYWV1Ed-6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 612
        },
        "outputId": "211aa66b-cc8d-48b3-b118-218c432c11d6"
      },
      "source": [
        "model_auto.summary()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>Statespace Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>                 <td>y</td>               <th>  No. Observations:  </th>   <td>6841</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>           <td>SARIMAX(2, 0, 2)x(1, 0, 1, 5)</td> <th>  Log Likelihood     </th> <td>-6836.991</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>                  <td>Wed, 01 Apr 2020</td>        <th>  AIC                </th> <td>13697.981</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                      <td>23:55:01</td>            <th>  BIC                </th> <td>13779.950</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>                   <td>01-11-1994</td>           <th>  HQIC               </th> <td>13726.259</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                         <td>- 03-31-2020</td>          <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>              <td>opg</td>              <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "       <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>intercept</th>  <td>   -0.0031</td> <td>    0.008</td> <td>   -0.399</td> <td> 0.690</td> <td>   -0.018</td> <td>    0.012</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>drift</th>      <td> -2.28e-06</td> <td> 2.34e-06</td> <td>   -0.974</td> <td> 0.330</td> <td>-6.87e-06</td> <td> 2.31e-06</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ret_spx</th>    <td>    0.1053</td> <td>    0.005</td> <td>   19.826</td> <td> 0.000</td> <td>    0.095</td> <td>    0.116</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ret_dax</th>    <td>    0.5618</td> <td>    0.005</td> <td>  120.001</td> <td> 0.000</td> <td>    0.553</td> <td>    0.571</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ret_nikkei</th> <td>    0.0706</td> <td>    0.004</td> <td>   17.777</td> <td> 0.000</td> <td>    0.063</td> <td>    0.078</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1</th>      <td>   -0.2066</td> <td>    0.088</td> <td>   -2.357</td> <td> 0.018</td> <td>   -0.378</td> <td>   -0.035</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2</th>      <td>    0.5427</td> <td>    0.054</td> <td>    9.988</td> <td> 0.000</td> <td>    0.436</td> <td>    0.649</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1</th>      <td>    0.1060</td> <td>    0.088</td> <td>    1.209</td> <td> 0.227</td> <td>   -0.066</td> <td>    0.278</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2</th>      <td>   -0.5764</td> <td>    0.052</td> <td>  -11.166</td> <td> 0.000</td> <td>   -0.678</td> <td>   -0.475</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.S.L5</th>    <td>    0.0520</td> <td>    0.325</td> <td>    0.160</td> <td> 0.873</td> <td>   -0.585</td> <td>    0.689</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.S.L5</th>    <td>   -0.0804</td> <td>    0.325</td> <td>   -0.247</td> <td> 0.805</td> <td>   -0.718</td> <td>    0.558</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>sigma2</th>     <td>    0.4306</td> <td>    0.004</td> <td>  105.327</td> <td> 0.000</td> <td>    0.423</td> <td>    0.439</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Ljung-Box (Q):</th>          <td>86.07</td> <th>  Jarque-Bera (JB):  </th> <td>16818.12</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Q):</th>                <td>0.00</td>  <th>  Prob(JB):          </th>   <td>0.00</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Heteroskedasticity (H):</th> <td>0.50</td>  <th>  Skew:              </th>   <td>0.22</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(H) (two-sided):</th>    <td>0.00</td>  <th>  Kurtosis:          </th>   <td>10.67</td> \n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                                 Statespace Model Results                                \n",
              "=========================================================================================\n",
              "Dep. Variable:                                 y   No. Observations:                 6841\n",
              "Model:             SARIMAX(2, 0, 2)x(1, 0, 1, 5)   Log Likelihood               -6836.991\n",
              "Date:                           Wed, 01 Apr 2020   AIC                          13697.981\n",
              "Time:                                   23:55:01   BIC                          13779.950\n",
              "Sample:                               01-11-1994   HQIC                         13726.259\n",
              "                                    - 03-31-2020                                         \n",
              "Covariance Type:                             opg                                         \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "intercept     -0.0031      0.008     -0.399      0.690      -0.018       0.012\n",
              "drift       -2.28e-06   2.34e-06     -0.974      0.330   -6.87e-06    2.31e-06\n",
              "ret_spx        0.1053      0.005     19.826      0.000       0.095       0.116\n",
              "ret_dax        0.5618      0.005    120.001      0.000       0.553       0.571\n",
              "ret_nikkei     0.0706      0.004     17.777      0.000       0.063       0.078\n",
              "ar.L1         -0.2066      0.088     -2.357      0.018      -0.378      -0.035\n",
              "ar.L2          0.5427      0.054      9.988      0.000       0.436       0.649\n",
              "ma.L1          0.1060      0.088      1.209      0.227      -0.066       0.278\n",
              "ma.L2         -0.5764      0.052    -11.166      0.000      -0.678      -0.475\n",
              "ar.S.L5        0.0520      0.325      0.160      0.873      -0.585       0.689\n",
              "ma.S.L5       -0.0804      0.325     -0.247      0.805      -0.718       0.558\n",
              "sigma2         0.4306      0.004    105.327      0.000       0.423       0.439\n",
              "===================================================================================\n",
              "Ljung-Box (Q):                       86.07   Jarque-Bera (JB):             16818.12\n",
              "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
              "Heteroskedasticity (H):               0.50   Skew:                             0.22\n",
              "Prob(H) (two-sided):                  0.00   Kurtosis:                        10.67\n",
              "===================================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yv_-RMtQHINM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 446
        },
        "outputId": "4cae4023-9030-4119-87e0-8b8731ab7778"
      },
      "source": [
        "plt.figure(figsize=(15,7))\n",
        "plt.plot(model_auto.resid())\n",
        "plt.title(\"ARIMA MODEL ERRORS\", size=25)\n",
        "plt.show()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AzJgxw9I5TkKA9tlnn6GiogIXXnghLr30Ul3vraurM5SuvrW1FRs3bjRVTjlC2adPnw4A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\nQqY7AD4NNcJagkLDg1DhcXs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F+Xvwl3eUh3BLTV2ovlB4MMmN/MnNAZYy+knvyqw7Z5VO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CgCoT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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1080x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}