6_The_auto_regressive_moving_average_(ARMA)_model.ipynb

{
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  "metadata": {
    "colab": {
      "name": "6. The auto regressive moving average (ARMA) model.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOvrSQ4h8p5Gc+F4nwnQsFp",
      "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/tanaymukherjee/Time-Series-Modeling/blob/master/6_The_auto_regressive_moving_average_(ARMA)_model.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rT1378K9iapT",
        "colab_type": "text"
      },
      "source": [
        "# Time Series Analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mM1WVU2Iie0K",
        "colab_type": "text"
      },
      "source": [
        "### Definition:\n",
        "A sequence of information which attaches a time period to each value."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PfyEkXFujSyW",
        "colab_type": "text"
      },
      "source": [
        "### Common Objective:\n",
        "1. Determining the stability of financial markets and the efficiency portfolios.\n",
        "2. Weather forcasting based on past records."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4z-_nucZluTz",
        "colab_type": "text"
      },
      "source": [
        "#### Import Libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bcw1FIsbiW-g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "d409cf17-ed54-4654-9842-d50b7fec41fa"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import statsmodels.graphics.tsaplots as sgt\n",
        "import statsmodels.tsa.stattools as sts\n",
        "from statsmodels.tsa.arima_model import ARMA\n",
        "from scipy.stats.distributions import chi2 \n",
        "from math import sqrt\n",
        "import seaborn as sns\n",
        "sns.set()"
      ],
      "execution_count": 1,
      "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": "RAJMSXfgmvue",
        "colab_type": "text"
      },
      "source": [
        "#### Mounting Google colab with personal GDrive"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dB-t7ZDCmRoR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "outputId": "16d41055-aa42-4e78-eab8-177c7993975e"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "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/gdrive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w1cVsLKCm155",
        "colab_type": "text"
      },
      "source": [
        "#### Checking the content in my GDrive witihin the working directory"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u8kooE9umgLn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!ls -ahl \"/content/gdrive/My Drive/Colab Notebooks/Data\""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pAtGYiuknPlx",
        "colab_type": "text"
      },
      "source": [
        "#### Read the dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VLKsgBinl0j6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = pd.read_csv(\"/content/gdrive/My Drive/Colab Notebooks/Data/Index2018.csv\")"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OMVAtJi7nmPy",
        "colab_type": "text"
      },
      "source": [
        "#### View the dataset summary"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IjdaO_ben1O2",
        "colab_type": "text"
      },
      "source": [
        "Date column includes the timen period where as the other features tell us the stability of market.\n",
        "\n",
        "1. SPX is US stock exchange by S&P 500\n",
        "2. DAX is German stock exchange by  DAX 30\n",
        "3. FTSE is UK stock exchange by FTSE 100\n",
        "4. NIKKEI is Japan stock exchange by NIKKEI 225"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ziSvBzNuDFhz",
        "colab_type": "text"
      },
      "source": [
        "#### Importing the Data and Pre-processing"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p9qL8ALMDJHq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "raw_csv_data = data\n",
        "df_comp=raw_csv_data.copy()\n",
        "df_comp.date = pd.to_datetime(df_comp.date, dayfirst = True)\n",
        "df_comp.set_index(\"date\", inplace=True)\n",
        "df_comp=df_comp.asfreq('b')\n",
        "df_comp=df_comp.fillna(method='ffill')"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e_tl1P_xuVX-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df_comp['market_value']=df_comp.ftse"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IatLdlZdym__",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "del df_comp['spx']\n",
        "del df_comp['dax']\n",
        "del df_comp['ftse']\n",
        "del df_comp['nikkei']\n",
        "size = int(len(df_comp)*0.8)\n",
        "df, df_test = df_comp.iloc[:size], df_comp.iloc[size:]"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZLsS5jvBPbsy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ux80mS3eLbB",
        "colab_type": "text"
      },
      "source": [
        "#### The LLR test"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RhRaWP3PeNYj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def LLR_test(mod_1, mod_2, DF = 1):\n",
        "    L1 = mod_1.fit().llf\n",
        "    L2 = mod_2.fit().llf\n",
        "    LR = (2*(L2-L1))    \n",
        "    p = chi2.sf(LR, DF).round(3)\n",
        "    return p"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WKokBZ2_P1Uv",
        "colab_type": "text"
      },
      "source": [
        "### Creating Returns"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P-zkJcYRP3vG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df['returns'] = df.market_value.pct_change(1)*100"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OBLpwEBzeQ-7",
        "colab_type": "text"
      },
      "source": [
        "#### ARMA(1,1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nTS4TAS7eTLR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 349
        },
        "outputId": "93ba1ad7-9eec-4e0f-8b8d-da4df570ae32"
      },
      "source": [
        "model_ret_ar_1_ma_1 = ARMA(df.returns[1:], order=(1,1))\n",
        "results_ret_ar_1_ma_1 = model_ret_ar_1_ma_1.fit()\n",
        "results_ret_ar_1_ma_1.summary()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(1, 1)</td>    <th>  Log Likelihood     </th> <td>-7916.500</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.171</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15841.000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:08:15</td>     <th>  BIC                </th> <td>15867.085</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15850.140</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.446</td> <td> 0.148</td> <td>   -0.007</td> <td>    0.045</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>    0.7649</td> <td>    0.067</td> <td>   11.349</td> <td> 0.000</td> <td>    0.633</td> <td>    0.897</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>   -0.8141</td> <td>    0.061</td> <td>  -13.406</td> <td> 0.000</td> <td>   -0.933</td> <td>   -0.695</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.3074</td> <td>          +0.0000j</td> <td>           1.3074</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.2284</td> <td>          +0.0000j</td> <td>           1.2284</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(1, 1)   Log Likelihood               -7916.500\n",
              "Method:                       css-mle   S.D. of innovations              1.171\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15841.000\n",
              "Time:                        03:08:15   BIC                          15867.085\n",
              "Sample:                    01-10-1994   HQIC                         15850.140\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.013      1.446      0.148      -0.007       0.045\n",
              "ar.L1.returns     0.7649      0.067     11.349      0.000       0.633       0.897\n",
              "ma.L1.returns    -0.8141      0.061    -13.406      0.000      -0.933      -0.695\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.3074           +0.0000j            1.3074            0.0000\n",
              "MA.1            1.2284           +0.0000j            1.2284            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bn0TWM1jP7mI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_ret_ar_1 = ARMA(df.returns[1:], order = (1,0))\n",
        "model_ret_ma_1 = ARMA(df.returns[1:], order = (0,1))"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mhda8thWP_go",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "print(\"\\nARMA vs AR \", LLR_test(model_ret_ar_1, model_ret_ar_1_ma_1))\n",
        "print(\"\\nARMA vs MA \", LLR_test(model_ret_ma_1, model_ret_ar_1_ma_1))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2vRtDqHKeggc",
        "colab_type": "text"
      },
      "source": [
        "### Higher-Lag ARMA Models\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a_FhuQsTQMaM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_ret_ar_3_ma_3 = ARMA(df.returns[1:], order=(3,3))\n",
        "results_ret_ar_3_ma_3 = model_ret_ar_3_ma_3.fit()"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uhe_h0GsQTVW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "LLR_test(model_ret_ar_1_ma_1, model_ret_ar_3_ma_3, DF = 4)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "boKxZX_RQWrW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 515
        },
        "outputId": "b5cf974b-b8fb-4ab3-d462-b8c242c86c6b"
      },
      "source": [
        "results_ret_ar_3_ma_3.summary()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(3, 3)</td>    <th>  Log Likelihood     </th> <td>-7893.515</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.166</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15803.030</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:10:14</td>     <th>  BIC                </th> <td>15855.199</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15821.310</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.395</td> <td> 0.163</td> <td>   -0.008</td> <td>    0.045</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>   -0.1898</td> <td>    0.104</td> <td>   -1.827</td> <td> 0.068</td> <td>   -0.393</td> <td>    0.014</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.returns</th> <td>   -0.2942</td> <td>    0.087</td> <td>   -3.389</td> <td> 0.001</td> <td>   -0.464</td> <td>   -0.124</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.returns</th> <td>    0.4459</td> <td>    0.138</td> <td>    3.225</td> <td> 0.001</td> <td>    0.175</td> <td>    0.717</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>    0.1707</td> <td>    0.099</td> <td>    1.726</td> <td> 0.084</td> <td>   -0.023</td> <td>    0.365</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.returns</th> <td>    0.2277</td> <td>    0.084</td> <td>    2.701</td> <td> 0.007</td> <td>    0.062</td> <td>    0.393</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.returns</th> <td>   -0.5432</td> <td>    0.127</td> <td>   -4.270</td> <td> 0.000</td> <td>   -0.793</td> <td>   -0.294</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -0.5168</td> <td>          -1.0283j</td> <td>           1.1508</td> <td>          -0.3241</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>          -0.5168</td> <td>          +1.0283j</td> <td>           1.1508</td> <td>           0.3241</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>           1.6932</td> <td>          -0.0000j</td> <td>           1.6932</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -0.5286</td> <td>          -0.9835j</td> <td>           1.1166</td> <td>          -0.3285</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>          -0.5286</td> <td>          +0.9835j</td> <td>           1.1166</td> <td>           0.3285</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>           1.4764</td> <td>          -0.0000j</td> <td>           1.4764</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(3, 3)   Log Likelihood               -7893.515\n",
              "Method:                       css-mle   S.D. of innovations              1.166\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15803.030\n",
              "Time:                        03:10:14   BIC                          15855.199\n",
              "Sample:                    01-10-1994   HQIC                         15821.310\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.014      1.395      0.163      -0.008       0.045\n",
              "ar.L1.returns    -0.1898      0.104     -1.827      0.068      -0.393       0.014\n",
              "ar.L2.returns    -0.2942      0.087     -3.389      0.001      -0.464      -0.124\n",
              "ar.L3.returns     0.4459      0.138      3.225      0.001       0.175       0.717\n",
              "ma.L1.returns     0.1707      0.099      1.726      0.084      -0.023       0.365\n",
              "ma.L2.returns     0.2277      0.084      2.701      0.007       0.062       0.393\n",
              "ma.L3.returns    -0.5432      0.127     -4.270      0.000      -0.793      -0.294\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -0.5168           -1.0283j            1.1508           -0.3241\n",
              "AR.2           -0.5168           +1.0283j            1.1508            0.3241\n",
              "AR.3            1.6932           -0.0000j            1.6932           -0.0000\n",
              "MA.1           -0.5286           -0.9835j            1.1166           -0.3285\n",
              "MA.2           -0.5286           +0.9835j            1.1166            0.3285\n",
              "MA.3            1.4764           -0.0000j            1.4764           -0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Avh2IbWSQaZm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 473
        },
        "outputId": "fb8683a0-e0fe-4e90-f42d-91053b9d5239"
      },
      "source": [
        "model_ret_ar_3_ma_2 = ARMA(df.returns[1:], order=(3,2))\n",
        "results_ret_ar_3_ma_2 = model_ret_ar_3_ma_2.fit()\n",
        "results_ret_ar_3_ma_2.summary()"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(3, 2)</td>    <th>  Log Likelihood     </th> <td>-7895.747</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.166</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15805.495</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:10:30</td>     <th>  BIC                </th> <td>15851.143</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15821.491</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0188</td> <td>    0.015</td> <td>    1.251</td> <td> 0.211</td> <td>   -0.011</td> <td>    0.048</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>   -0.6785</td> <td>    0.087</td> <td>   -7.799</td> <td> 0.000</td> <td>   -0.849</td> <td>   -0.508</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.returns</th> <td>   -0.5088</td> <td>    0.139</td> <td>   -3.670</td> <td> 0.000</td> <td>   -0.780</td> <td>   -0.237</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.returns</th> <td>   -0.1141</td> <td>    0.015</td> <td>   -7.655</td> <td> 0.000</td> <td>   -0.143</td> <td>   -0.085</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>    0.6568</td> <td>    0.087</td> <td>    7.536</td> <td> 0.000</td> <td>    0.486</td> <td>    0.828</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.returns</th> <td>    0.4474</td> <td>    0.141</td> <td>    3.175</td> <td> 0.002</td> <td>    0.171</td> <td>    0.724</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -0.4929</td> <td>          -1.5100j</td> <td>           1.5885</td> <td>          -0.3002</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>          -0.4929</td> <td>          +1.5100j</td> <td>           1.5885</td> <td>           0.3002</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>          -3.4749</td> <td>          -0.0000j</td> <td>           3.4749</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -0.7340</td> <td>          -1.3025j</td> <td>           1.4951</td> <td>          -0.3317</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>          -0.7340</td> <td>          +1.3025j</td> <td>           1.4951</td> <td>           0.3317</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(3, 2)   Log Likelihood               -7895.747\n",
              "Method:                       css-mle   S.D. of innovations              1.166\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15805.495\n",
              "Time:                        03:10:30   BIC                          15851.143\n",
              "Sample:                    01-10-1994   HQIC                         15821.491\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0188      0.015      1.251      0.211      -0.011       0.048\n",
              "ar.L1.returns    -0.6785      0.087     -7.799      0.000      -0.849      -0.508\n",
              "ar.L2.returns    -0.5088      0.139     -3.670      0.000      -0.780      -0.237\n",
              "ar.L3.returns    -0.1141      0.015     -7.655      0.000      -0.143      -0.085\n",
              "ma.L1.returns     0.6568      0.087      7.536      0.000       0.486       0.828\n",
              "ma.L2.returns     0.4474      0.141      3.175      0.002       0.171       0.724\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -0.4929           -1.5100j            1.5885           -0.3002\n",
              "AR.2           -0.4929           +1.5100j            1.5885            0.3002\n",
              "AR.3           -3.4749           -0.0000j            3.4749           -0.5000\n",
              "MA.1           -0.7340           -1.3025j            1.4951           -0.3317\n",
              "MA.2           -0.7340           +1.3025j            1.4951            0.3317\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dUcaMLrvQcix",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 473
        },
        "outputId": "5cc9a3c2-eb5b-4630-c082-b134e9a39c50"
      },
      "source": [
        "model_ret_ar_2_ma_3 = ARMA(df.returns[1:], order=(2,3))\n",
        "results_ret_ar_2_ma_3 = model_ret_ar_2_ma_3.fit()\n",
        "results_ret_ar_2_ma_3.summary()"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(2, 3)</td>    <th>  Log Likelihood     </th> <td>-7895.587</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.166</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15805.174</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:10:40</td>     <th>  BIC                </th> <td>15850.823</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15821.170</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.015</td> <td>    1.276</td> <td> 0.202</td> <td>   -0.010</td> <td>    0.048</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>   -0.5605</td> <td>    0.090</td> <td>   -6.245</td> <td> 0.000</td> <td>   -0.736</td> <td>   -0.385</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.returns</th> <td>   -0.4187</td> <td>    0.193</td> <td>   -2.172</td> <td> 0.030</td> <td>   -0.797</td> <td>   -0.041</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>    0.5378</td> <td>    0.090</td> <td>    6.000</td> <td> 0.000</td> <td>    0.362</td> <td>    0.714</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.returns</th> <td>    0.3540</td> <td>    0.195</td> <td>    1.818</td> <td> 0.069</td> <td>   -0.028</td> <td>    0.736</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.returns</th> <td>   -0.1158</td> <td>    0.016</td> <td>   -7.369</td> <td> 0.000</td> <td>   -0.147</td> <td>   -0.085</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -0.6694</td> <td>          -1.3930j</td> <td>           1.5455</td> <td>          -0.3213</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>          -0.6694</td> <td>          +1.3930j</td> <td>           1.5455</td> <td>           0.3213</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -0.7270</td> <td>          -1.1772j</td> <td>           1.3836</td> <td>          -0.3381</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>          -0.7270</td> <td>          +1.1772j</td> <td>           1.3836</td> <td>           0.3381</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>           4.5096</td> <td>          -0.0000j</td> <td>           4.5096</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(2, 3)   Log Likelihood               -7895.587\n",
              "Method:                       css-mle   S.D. of innovations              1.166\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15805.174\n",
              "Time:                        03:10:40   BIC                          15850.823\n",
              "Sample:                    01-10-1994   HQIC                         15821.170\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.015      1.276      0.202      -0.010       0.048\n",
              "ar.L1.returns    -0.5605      0.090     -6.245      0.000      -0.736      -0.385\n",
              "ar.L2.returns    -0.4187      0.193     -2.172      0.030      -0.797      -0.041\n",
              "ma.L1.returns     0.5378      0.090      6.000      0.000       0.362       0.714\n",
              "ma.L2.returns     0.3540      0.195      1.818      0.069      -0.028       0.736\n",
              "ma.L3.returns    -0.1158      0.016     -7.369      0.000      -0.147      -0.085\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -0.6694           -1.3930j            1.5455           -0.3213\n",
              "AR.2           -0.6694           +1.3930j            1.5455            0.3213\n",
              "MA.1           -0.7270           -1.1772j            1.3836           -0.3381\n",
              "MA.2           -0.7270           +1.1772j            1.3836            0.3381\n",
              "MA.3            4.5096           -0.0000j            4.5096           -0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nSfbnQhIQeYe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "LLR_test(model_ret_ar_2_ma_3, model_ret_ar_3_ma_3)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qnv99wd5QfRG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 432
        },
        "outputId": "e876a66f-c0e9-452f-be06-db324ec5f5e1"
      },
      "source": [
        "model_ret_ar_3_ma_1 = ARMA(df.returns[1:], order=(3,1))\n",
        "results_ret_ar_3_ma_1 = model_ret_ar_3_ma_1.fit()\n",
        "results_ret_ar_3_ma_1.summary()"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(3, 1)</td>    <th>  Log Likelihood     </th> <td>-7899.072</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.167</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15810.144</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:10:52</td>     <th>  BIC                </th> <td>15849.271</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15823.855</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.015</td> <td>    1.298</td> <td> 0.194</td> <td>   -0.010</td> <td>    0.047</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>   -0.5077</td> <td>    0.088</td> <td>   -5.769</td> <td> 0.000</td> <td>   -0.680</td> <td>   -0.335</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.returns</th> <td>   -0.0638</td> <td>    0.016</td> <td>   -4.023</td> <td> 0.000</td> <td>   -0.095</td> <td>   -0.033</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.returns</th> <td>   -0.1102</td> <td>    0.014</td> <td>   -7.850</td> <td> 0.000</td> <td>   -0.138</td> <td>   -0.083</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>    0.4839</td> <td>    0.088</td> <td>    5.500</td> <td> 0.000</td> <td>    0.311</td> <td>    0.656</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -1.5095</td> <td>          -0.0000j</td> <td>           1.5095</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           0.4653</td> <td>          -2.4076j</td> <td>           2.4521</td> <td>          -0.2196</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>           0.4653</td> <td>          +2.4076j</td> <td>           2.4521</td> <td>           0.2196</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -2.0668</td> <td>          +0.0000j</td> <td>           2.0668</td> <td>           0.5000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(3, 1)   Log Likelihood               -7899.072\n",
              "Method:                       css-mle   S.D. of innovations              1.167\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15810.144\n",
              "Time:                        03:10:52   BIC                          15849.271\n",
              "Sample:                    01-10-1994   HQIC                         15823.855\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.015      1.298      0.194      -0.010       0.047\n",
              "ar.L1.returns    -0.5077      0.088     -5.769      0.000      -0.680      -0.335\n",
              "ar.L2.returns    -0.0638      0.016     -4.023      0.000      -0.095      -0.033\n",
              "ar.L3.returns    -0.1102      0.014     -7.850      0.000      -0.138      -0.083\n",
              "ma.L1.returns     0.4839      0.088      5.500      0.000       0.311       0.656\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -1.5095           -0.0000j            1.5095           -0.5000\n",
              "AR.2            0.4653           -2.4076j            2.4521           -0.2196\n",
              "AR.3            0.4653           +2.4076j            2.4521            0.2196\n",
              "MA.1           -2.0668           +0.0000j            2.0668            0.5000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_ktL8sO2Qh7B",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "LLR_test(model_ret_ar_3_ma_1, model_ret_ar_3_ma_2)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wCvNwYBWQiW4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 432
        },
        "outputId": "d3f03e14-a8cc-46da-804b-981832af579f"
      },
      "source": [
        "model_ret_ar_2_ma_2 = ARMA(df.returns[1:], order=(2,2))\n",
        "results_ret_ar_2_ma_2 = model_ret_ar_2_ma_2.fit()\n",
        "results_ret_ar_2_ma_2.summary()"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(2, 2)</td>    <th>  Log Likelihood     </th> <td>-7913.223</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.170</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15838.446</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:11:06</td>     <th>  BIC                </th> <td>15877.573</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15852.156</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.394</td> <td> 0.163</td> <td>   -0.008</td> <td>    0.045</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>    0.7820</td> <td>    0.238</td> <td>    3.284</td> <td> 0.001</td> <td>    0.315</td> <td>    1.249</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.returns</th> <td>   -0.1563</td> <td>    0.177</td> <td>   -0.884</td> <td> 0.377</td> <td>   -0.503</td> <td>    0.190</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>   -0.8105</td> <td>    0.239</td> <td>   -3.388</td> <td> 0.001</td> <td>   -1.279</td> <td>   -0.342</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.returns</th> <td>    0.1177</td> <td>    0.187</td> <td>    0.628</td> <td> 0.530</td> <td>   -0.250</td> <td>    0.485</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           2.5017</td> <td>          -0.3739j</td> <td>           2.5295</td> <td>          -0.0236</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           2.5017</td> <td>          +0.3739j</td> <td>           2.5295</td> <td>           0.0236</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.6107</td> <td>          +0.0000j</td> <td>           1.6107</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>           5.2737</td> <td>          +0.0000j</td> <td>           5.2737</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(2, 2)   Log Likelihood               -7913.223\n",
              "Method:                       css-mle   S.D. of innovations              1.170\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15838.446\n",
              "Time:                        03:11:06   BIC                          15877.573\n",
              "Sample:                    01-10-1994   HQIC                         15852.156\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.014      1.394      0.163      -0.008       0.045\n",
              "ar.L1.returns     0.7820      0.238      3.284      0.001       0.315       1.249\n",
              "ar.L2.returns    -0.1563      0.177     -0.884      0.377      -0.503       0.190\n",
              "ma.L1.returns    -0.8105      0.239     -3.388      0.001      -1.279      -0.342\n",
              "ma.L2.returns     0.1177      0.187      0.628      0.530      -0.250       0.485\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            2.5017           -0.3739j            2.5295           -0.0236\n",
              "AR.2            2.5017           +0.3739j            2.5295            0.0236\n",
              "MA.1            1.6107           +0.0000j            1.6107            0.0000\n",
              "MA.2            5.2737           +0.0000j            5.2737            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0PvQK0jvQkWA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 432
        },
        "outputId": "e9f300a7-656c-4ce1-ab1c-31578ae8c969"
      },
      "source": [
        "model_ret_ar_1_ma_3 = ARMA(df.returns[1:], order=(1,3))\n",
        "results_ret_ar_1_ma_3 = model_ret_ar_1_ma_3.fit()\n",
        "results_ret_ar_1_ma_3.summary()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(1, 3)</td>    <th>  Log Likelihood     </th> <td>-7896.838</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.167</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15805.676</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:11:12</td>     <th>  BIC                </th> <td>15844.803</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15819.386</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.014</td> <td>    1.332</td> <td> 0.183</td> <td>   -0.009</td> <td>    0.047</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>   -0.4699</td> <td>    0.096</td> <td>   -4.901</td> <td> 0.000</td> <td>   -0.658</td> <td>   -0.282</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>    0.4474</td> <td>    0.095</td> <td>    4.691</td> <td> 0.000</td> <td>    0.260</td> <td>    0.634</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.returns</th> <td>   -0.0637</td> <td>    0.015</td> <td>   -4.113</td> <td> 0.000</td> <td>   -0.094</td> <td>   -0.033</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.returns</th> <td>   -0.1182</td> <td>    0.014</td> <td>   -8.200</td> <td> 0.000</td> <td>   -0.146</td> <td>   -0.090</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -2.1282</td> <td>          +0.0000j</td> <td>           2.1282</td> <td>           0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -1.4882</td> <td>          -1.1206j</td> <td>           1.8629</td> <td>          -0.3973</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>          -1.4882</td> <td>          +1.1206j</td> <td>           1.8629</td> <td>           0.3973</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>           2.4376</td> <td>          -0.0000j</td> <td>           2.4376</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(1, 3)   Log Likelihood               -7896.838\n",
              "Method:                       css-mle   S.D. of innovations              1.167\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15805.676\n",
              "Time:                        03:11:12   BIC                          15844.803\n",
              "Sample:                    01-10-1994   HQIC                         15819.386\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.014      1.332      0.183      -0.009       0.047\n",
              "ar.L1.returns    -0.4699      0.096     -4.901      0.000      -0.658      -0.282\n",
              "ma.L1.returns     0.4474      0.095      4.691      0.000       0.260       0.634\n",
              "ma.L2.returns    -0.0637      0.015     -4.113      0.000      -0.094      -0.033\n",
              "ma.L3.returns    -0.1182      0.014     -8.200      0.000      -0.146      -0.090\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -2.1282           +0.0000j            2.1282            0.5000\n",
              "MA.1           -1.4882           -1.1206j            1.8629           -0.3973\n",
              "MA.2           -1.4882           +1.1206j            1.8629            0.3973\n",
              "MA.3            2.4376           -0.0000j            2.4376           -0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g5kCTGPPQmBl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "d734fcd5-5ce6-4870-b3b4-16946c4a3f7b"
      },
      "source": [
        "print(\"\\n ARMA(3,2): \\tLL = \", results_ret_ar_3_ma_2.llf, \"\\tAIC = \", results_ret_ar_3_ma_2.aic)\n",
        "print(\"\\n ARMA(1,3): \\tLL = \", results_ret_ar_1_ma_3.llf, \"\\tAIC = \", results_ret_ar_1_ma_3.aic)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            " ARMA(3,2): \tLL =  -7895.7474585145965 \tAIC =  15805.494917029193\n",
            "\n",
            " ARMA(1,3): \tLL =  -7896.837893752801 \tAIC =  15805.675787505603\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tjIG4l6nQpC_",
        "colab_type": "text"
      },
      "source": [
        "### Residuals for Returns"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-Pm-0Gl3QqA9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df['res_ret_ar_3_ma_2'] = results_ret_ar_3_ma_2.resid[1:]"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "83dFY6vIQrX-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        },
        "outputId": "f428ea5f-8b49-42e8-f321-4907f7bf8d2c"
      },
      "source": [
        "df.res_ret_ar_3_ma_2.plot(figsize = (25,5))\n",
        "plt.title(\"Residuals of Returns\", size=24)\n",
        "plt.show()"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1800x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1_Rx-qBIQuaa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "41915755-1c6d-4f51-bfc6-4ec0d5598949"
      },
      "source": [
        "sgt.plot_acf(df.res_ret_ar_3_ma_2[2:], zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals for Returns\",size=24)\n",
        "plt.show()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Rh3F40oQxyZ",
        "colab_type": "text"
      },
      "source": [
        "### Re-evaluating Model Selection"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GnNOdbVKQzdm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 681
        },
        "outputId": "2bb92adb-82eb-4a9f-ba27-7f7e886b0cc8"
      },
      "source": [
        "model_ret_ar_5_ma_5 = ARMA(df.returns[1:], order=(5,5))\n",
        "results_ret_ar_5_ma_5 = model_ret_ar_5_ma_5.fit()\n",
        "results_ret_ar_5_ma_5.summary()"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(5, 5)</td>    <th>  Log Likelihood     </th> <td>-7882.160</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.163</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15788.321</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:12:30</td>     <th>  BIC                </th> <td>15866.575</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15815.742</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.402</td> <td> 0.161</td> <td>   -0.008</td> <td>    0.045</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>   -0.0684</td> <td>    0.140</td> <td>   -0.490</td> <td> 0.624</td> <td>   -0.342</td> <td>    0.205</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.returns</th> <td>   -0.6722</td> <td>    0.146</td> <td>   -4.603</td> <td> 0.000</td> <td>   -0.958</td> <td>   -0.386</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.returns</th> <td>   -0.1152</td> <td>    0.141</td> <td>   -0.817</td> <td> 0.414</td> <td>   -0.392</td> <td>    0.161</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L4.returns</th> <td>    0.1779</td> <td>    0.129</td> <td>    1.381</td> <td> 0.167</td> <td>   -0.075</td> <td>    0.430</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L5.returns</th> <td>    0.1215</td> <td>    0.107</td> <td>    1.132</td> <td> 0.258</td> <td>   -0.089</td> <td>    0.332</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>    0.0443</td> <td>    0.138</td> <td>    0.322</td> <td> 0.748</td> <td>   -0.226</td> <td>    0.314</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.returns</th> <td>    0.6223</td> <td>    0.144</td> <td>    4.321</td> <td> 0.000</td> <td>    0.340</td> <td>    0.905</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.returns</th> <td>    0.0107</td> <td>    0.136</td> <td>    0.079</td> <td> 0.937</td> <td>   -0.256</td> <td>    0.277</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L4.returns</th> <td>   -0.1753</td> <td>    0.122</td> <td>   -1.436</td> <td> 0.151</td> <td>   -0.415</td> <td>    0.064</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L5.returns</th> <td>   -0.2240</td> <td>    0.104</td> <td>   -2.148</td> <td> 0.032</td> <td>   -0.428</td> <td>   -0.020</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           0.0870</td> <td>          -1.0364j</td> <td>           1.0401</td> <td>          -0.2367</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           0.0870</td> <td>          +1.0364j</td> <td>           1.0401</td> <td>           0.2367</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>           1.7715</td> <td>          -0.0000j</td> <td>           1.7715</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.4</th> <td>          -1.7050</td> <td>          -1.1784j</td> <td>           2.0726</td> <td>          -0.4038</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.5</th> <td>          -1.7050</td> <td>          +1.1784j</td> <td>           2.0726</td> <td>           0.4038</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           0.1033</td> <td>          -1.0434j</td> <td>           1.0485</td> <td>          -0.2343</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>           0.1033</td> <td>          +1.0434j</td> <td>           1.0485</td> <td>           0.2343</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>           1.4855</td> <td>          -0.0000j</td> <td>           1.4855</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.4</th> <td>          -1.2373</td> <td>          -1.0965j</td> <td>           1.6532</td> <td>          -0.3846</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.5</th> <td>          -1.2373</td> <td>          +1.0965j</td> <td>           1.6532</td> <td>           0.3846</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(5, 5)   Log Likelihood               -7882.160\n",
              "Method:                       css-mle   S.D. of innovations              1.163\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15788.321\n",
              "Time:                        03:12:30   BIC                          15866.575\n",
              "Sample:                    01-10-1994   HQIC                         15815.742\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.013      1.402      0.161      -0.008       0.045\n",
              "ar.L1.returns    -0.0684      0.140     -0.490      0.624      -0.342       0.205\n",
              "ar.L2.returns    -0.6722      0.146     -4.603      0.000      -0.958      -0.386\n",
              "ar.L3.returns    -0.1152      0.141     -0.817      0.414      -0.392       0.161\n",
              "ar.L4.returns     0.1779      0.129      1.381      0.167      -0.075       0.430\n",
              "ar.L5.returns     0.1215      0.107      1.132      0.258      -0.089       0.332\n",
              "ma.L1.returns     0.0443      0.138      0.322      0.748      -0.226       0.314\n",
              "ma.L2.returns     0.6223      0.144      4.321      0.000       0.340       0.905\n",
              "ma.L3.returns     0.0107      0.136      0.079      0.937      -0.256       0.277\n",
              "ma.L4.returns    -0.1753      0.122     -1.436      0.151      -0.415       0.064\n",
              "ma.L5.returns    -0.2240      0.104     -2.148      0.032      -0.428      -0.020\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            0.0870           -1.0364j            1.0401           -0.2367\n",
              "AR.2            0.0870           +1.0364j            1.0401            0.2367\n",
              "AR.3            1.7715           -0.0000j            1.7715           -0.0000\n",
              "AR.4           -1.7050           -1.1784j            2.0726           -0.4038\n",
              "AR.5           -1.7050           +1.1784j            2.0726            0.4038\n",
              "MA.1            0.1033           -1.0434j            1.0485           -0.2343\n",
              "MA.2            0.1033           +1.0434j            1.0485            0.2343\n",
              "MA.3            1.4855           -0.0000j            1.4855           -0.0000\n",
              "MA.4           -1.2373           -1.0965j            1.6532           -0.3846\n",
              "MA.5           -1.2373           +1.0965j            1.6532            0.3846\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fod5HUlSQ2Ix",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 515
        },
        "outputId": "df6e4757-826d-45b9-fd4e-e1a04ea81a3e"
      },
      "source": [
        "model_ret_ar_5_ma_1 = ARMA(df.returns[1:], order=(5,1))\n",
        "results_ret_ar_5_ma_1 = model_ret_ar_5_ma_1.fit()\n",
        "results_ret_ar_5_ma_1.summary()"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(5, 1)</td>    <th>  Log Likelihood     </th> <td>-7889.311</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.165</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15794.623</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:12:38</td>     <th>  BIC                </th> <td>15846.792</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15812.903</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.407</td> <td> 0.159</td> <td>   -0.007</td> <td>    0.045</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>    0.3440</td> <td>    0.131</td> <td>    2.624</td> <td> 0.009</td> <td>    0.087</td> <td>    0.601</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.returns</th> <td>   -0.0458</td> <td>    0.015</td> <td>   -3.005</td> <td> 0.003</td> <td>   -0.076</td> <td>   -0.016</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.returns</th> <td>   -0.0652</td> <td>    0.016</td> <td>   -4.010</td> <td> 0.000</td> <td>   -0.097</td> <td>   -0.033</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L4.returns</th> <td>    0.0741</td> <td>    0.018</td> <td>    4.068</td> <td> 0.000</td> <td>    0.038</td> <td>    0.110</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L5.returns</th> <td>   -0.0813</td> <td>    0.014</td> <td>   -5.688</td> <td> 0.000</td> <td>   -0.109</td> <td>   -0.053</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>   -0.3673</td> <td>    0.131</td> <td>   -2.801</td> <td> 0.005</td> <td>   -0.624</td> <td>   -0.110</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -1.6158</td> <td>          -0.0000j</td> <td>           1.6158</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           1.3793</td> <td>          -0.8614j</td> <td>           1.6261</td> <td>          -0.0888</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>           1.3793</td> <td>          +0.8614j</td> <td>           1.6261</td> <td>           0.0888</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.4</th> <td>          -0.1156</td> <td>          -1.6929j</td> <td>           1.6968</td> <td>          -0.2608</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.5</th> <td>          -0.1156</td> <td>          +1.6929j</td> <td>           1.6968</td> <td>           0.2608</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           2.7223</td> <td>          +0.0000j</td> <td>           2.7223</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(5, 1)   Log Likelihood               -7889.311\n",
              "Method:                       css-mle   S.D. of innovations              1.165\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15794.623\n",
              "Time:                        03:12:38   BIC                          15846.792\n",
              "Sample:                    01-10-1994   HQIC                         15812.903\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.013      1.407      0.159      -0.007       0.045\n",
              "ar.L1.returns     0.3440      0.131      2.624      0.009       0.087       0.601\n",
              "ar.L2.returns    -0.0458      0.015     -3.005      0.003      -0.076      -0.016\n",
              "ar.L3.returns    -0.0652      0.016     -4.010      0.000      -0.097      -0.033\n",
              "ar.L4.returns     0.0741      0.018      4.068      0.000       0.038       0.110\n",
              "ar.L5.returns    -0.0813      0.014     -5.688      0.000      -0.109      -0.053\n",
              "ma.L1.returns    -0.3673      0.131     -2.801      0.005      -0.624      -0.110\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -1.6158           -0.0000j            1.6158           -0.5000\n",
              "AR.2            1.3793           -0.8614j            1.6261           -0.0888\n",
              "AR.3            1.3793           +0.8614j            1.6261            0.0888\n",
              "AR.4           -0.1156           -1.6929j            1.6968           -0.2608\n",
              "AR.5           -0.1156           +1.6929j            1.6968            0.2608\n",
              "MA.1            2.7223           +0.0000j            2.7223            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1tOxv3DBQ6o2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 515
        },
        "outputId": "1449a54d-b16b-4b85-e4b3-5ce5cb13ef60"
      },
      "source": [
        "model_ret_ar_1_ma_5 = ARMA(df.returns[1:], order=(1,5))\n",
        "results_ret_ar_1_ma_5 = model_ret_ar_1_ma_5.fit()\n",
        "results_ret_ar_1_ma_5.summary()"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>returns</td>     <th>  No. Observations:  </th>   <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(1, 5)</td>    <th>  Log Likelihood     </th> <td>-7890.973</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.165</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th> <td>15797.947</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:12:44</td>     <th>  BIC                </th> <td>15850.116</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th> <td>15816.228</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>         <td>    0.0189</td> <td>    0.013</td> <td>    1.419</td> <td> 0.156</td> <td>   -0.007</td> <td>    0.045</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.returns</th> <td>    0.3285</td> <td>    0.152</td> <td>    2.159</td> <td> 0.031</td> <td>    0.030</td> <td>    0.627</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.returns</th> <td>   -0.3534</td> <td>    0.152</td> <td>   -2.332</td> <td> 0.020</td> <td>   -0.650</td> <td>   -0.056</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.returns</th> <td>   -0.0404</td> <td>    0.015</td> <td>   -2.624</td> <td> 0.009</td> <td>   -0.071</td> <td>   -0.010</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.returns</th> <td>   -0.0679</td> <td>    0.017</td> <td>   -4.022</td> <td> 0.000</td> <td>   -0.101</td> <td>   -0.035</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L4.returns</th> <td>    0.0742</td> <td>    0.020</td> <td>    3.771</td> <td> 0.000</td> <td>    0.036</td> <td>    0.113</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L5.returns</th> <td>   -0.0683</td> <td>    0.015</td> <td>   -4.660</td> <td> 0.000</td> <td>   -0.097</td> <td>   -0.040</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           3.0442</td> <td>          +0.0000j</td> <td>           3.0442</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -1.1897</td> <td>          -1.1548j</td> <td>           1.6580</td> <td>          -0.3774</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>          -1.1897</td> <td>          +1.1548j</td> <td>           1.6580</td> <td>           0.3774</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>           1.5041</td> <td>          -0.0000j</td> <td>           1.5041</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.4</th> <td>           0.9809</td> <td>          -1.6057j</td> <td>           1.8815</td> <td>          -0.1627</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.5</th> <td>           0.9809</td> <td>          +1.6057j</td> <td>           1.8815</td> <td>           0.1627</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                returns   No. Observations:                 5020\n",
              "Model:                     ARMA(1, 5)   Log Likelihood               -7890.973\n",
              "Method:                       css-mle   S.D. of innovations              1.165\n",
              "Date:                Wed, 17 Jun 2020   AIC                          15797.947\n",
              "Time:                        03:12:44   BIC                          15850.116\n",
              "Sample:                    01-10-1994   HQIC                         15816.228\n",
              "                         - 04-05-2013                                         \n",
              "=================================================================================\n",
              "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------\n",
              "const             0.0189      0.013      1.419      0.156      -0.007       0.045\n",
              "ar.L1.returns     0.3285      0.152      2.159      0.031       0.030       0.627\n",
              "ma.L1.returns    -0.3534      0.152     -2.332      0.020      -0.650      -0.056\n",
              "ma.L2.returns    -0.0404      0.015     -2.624      0.009      -0.071      -0.010\n",
              "ma.L3.returns    -0.0679      0.017     -4.022      0.000      -0.101      -0.035\n",
              "ma.L4.returns     0.0742      0.020      3.771      0.000       0.036       0.113\n",
              "ma.L5.returns    -0.0683      0.015     -4.660      0.000      -0.097      -0.040\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            3.0442           +0.0000j            3.0442            0.0000\n",
              "MA.1           -1.1897           -1.1548j            1.6580           -0.3774\n",
              "MA.2           -1.1897           +1.1548j            1.6580            0.3774\n",
              "MA.3            1.5041           -0.0000j            1.5041           -0.0000\n",
              "MA.4            0.9809           -1.6057j            1.8815           -0.1627\n",
              "MA.5            0.9809           +1.6057j            1.8815            0.1627\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t4SZm5DmQ8z7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "26f6a15b-25b6-4cb3-ac7c-01f572993dba"
      },
      "source": [
        "print(\"ARMA(5,1):  \\t LL = \",results_ret_ar_5_ma_1.llf,\"\\t AIC = \",results_ret_ar_5_ma_1.aic)\n",
        "print(\"ARMA(1,5):  \\t LL = \",results_ret_ar_1_ma_5.llf,\"\\t AIC = \",results_ret_ar_1_ma_5.aic)"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARMA(5,1):  \t LL =  -7889.311282945847 \t AIC =  15794.622565891694\n",
            "ARMA(1,5):  \t LL =  -7890.973460209621 \t AIC =  15797.946920419243\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "slkS9xY3Q-Zf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "5865f08a-78e2-4366-c27a-6a12c408a82b"
      },
      "source": [
        "print(\"ARMA(3,2):  \\t LL = \",results_ret_ar_3_ma_2.llf,\"\\t AIC = \",results_ret_ar_3_ma_2.aic)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARMA(3,2):  \t LL =  -7895.7474585145965 \t AIC =  15805.494917029193\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Oh72FxALRAou",
        "colab_type": "text"
      },
      "source": [
        "### Residuals for the New Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n71wHb4qRBZ7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df['res_ret_ar_5_ma_1'] = results_ret_ar_5_ma_1.resid"
      ],
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O-FtKFNFRCq7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "c089b38f-8d5f-4b72-f9a9-8357e62fdb99"
      },
      "source": [
        "sgt.plot_acf(df.res_ret_ar_5_ma_1[1:], zero = False, lags = 40)\n",
        "plt.title(\"ACF of Residuals for Returns\",size=24)\n",
        "plt.show()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pLa9Z6V7RFjK",
        "colab_type": "text"
      },
      "source": [
        "### ARMA Models for Prices"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cGvxMpkSRGdU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "outputId": "17084a16-81fe-4c5c-94f5-bf079463b8e9"
      },
      "source": [
        "sgt.plot_acf(df.market_value, unbiased=True, zero = False, lags = 40)\n",
        "plt.title(\"Autocorrelation Function for Prices\",size=20)\n",
        "plt.show()"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RT6L_Df_RIr-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "outputId": "8b06bd81-bfdc-43db-ad94-1953abaff7a4"
      },
      "source": [
        "sgt.plot_pacf(df.market_value, lags = 40, alpha = 0.05, zero = False , method = ('ols'))\n",
        "plt.title(\"Partial Autocorrelation Function for Prices\",size=20)\n",
        "plt.show()"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IoTlV6T9RKBA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 349
        },
        "outputId": "1337b1fc-cc69-4443-df0b-938cc4610bab"
      },
      "source": [
        "model_ar_1_ma_1 = ARMA(df.market_value, order=(1,1))\n",
        "results_ar_1_ma_1 = model_ar_1_ma_1.fit()\n",
        "results_ar_1_ma_1.summary()"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(1, 1)</td>    <th>  Log Likelihood     </th> <td>-27621.792</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>59.248</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th>  <td>55251.584</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:13:45</td>     <th>  BIC                </th>  <td>55277.670</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55260.725</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5101.4137</td> <td>  497.008</td> <td>   10.264</td> <td> 0.000</td> <td> 4127.296</td> <td> 6075.532</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.market_value</th> <td>    0.9985</td> <td>    0.001</td> <td> 1321.326</td> <td> 0.000</td> <td>    0.997</td> <td>    1.000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.market_value</th> <td>   -0.0191</td> <td>    0.015</td> <td>   -1.278</td> <td> 0.201</td> <td>   -0.048</td> <td>    0.010</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.0015</td> <td>          +0.0000j</td> <td>           1.0015</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          52.3402</td> <td>          +0.0000j</td> <td>          52.3402</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:           market_value   No. Observations:                 5021\n",
              "Model:                     ARMA(1, 1)   Log Likelihood              -27621.792\n",
              "Method:                       css-mle   S.D. of innovations             59.248\n",
              "Date:                Wed, 17 Jun 2020   AIC                          55251.584\n",
              "Time:                        03:13:45   BIC                          55277.670\n",
              "Sample:                    01-07-1994   HQIC                         55260.725\n",
              "                         - 04-05-2013                                         \n",
              "======================================================================================\n",
              "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
              "--------------------------------------------------------------------------------------\n",
              "const               5101.4137    497.008     10.264      0.000    4127.296    6075.532\n",
              "ar.L1.market_value     0.9985      0.001   1321.326      0.000       0.997       1.000\n",
              "ma.L1.market_value    -0.0191      0.015     -1.278      0.201      -0.048       0.010\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.0015           +0.0000j            1.0015            0.0000\n",
              "MA.1           52.3402           +0.0000j           52.3402            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZkwgMmxrRLaa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df['res_ar_1_ma_1'] = results_ar_1_ma_1.resid"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xQuEoy_NRMrP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "outputId": "ff7c8292-c035-4331-ab9d-fa17bfcbbba5"
      },
      "source": [
        "sgt.plot_acf(df.res_ar_1_ma_1, zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals of Prices\",size=20)\n",
        "plt.show()"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HJtjpYccROff",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 765
        },
        "outputId": "a2b6b20c-dcfd-47c3-fe52-eecb47b96ed6"
      },
      "source": [
        "model_ar_6_ma_6 = ARMA(df.market_value, order=(6,6))\n",
        "results_ar_6_ma_6 = model_ar_6_ma_6.fit(start_ar_lags = 11)\n",
        "results_ar_6_ma_6.summary()"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(6, 6)</td>    <th>  Log Likelihood     </th> <td>-27587.932</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>58.849</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th>  <td>55203.864</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:14:15</td>     <th>  BIC                </th>  <td>55295.164</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55235.856</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5089.6477</td> <td>  568.179</td> <td>    8.958</td> <td> 0.000</td> <td> 3976.037</td> <td> 6203.259</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.market_value</th> <td>    1.9275</td> <td>    0.032</td> <td>   59.960</td> <td> 0.000</td> <td>    1.864</td> <td>    1.990</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.market_value</th> <td>   -1.7357</td> <td>    0.040</td> <td>  -43.372</td> <td> 0.000</td> <td>   -1.814</td> <td>   -1.657</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.market_value</th> <td>    1.2673</td> <td>    0.034</td> <td>   36.745</td> <td> 0.000</td> <td>    1.200</td> <td>    1.335</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L4.market_value</th> <td>   -0.2372</td> <td>    0.159</td> <td>   -1.496</td> <td> 0.135</td> <td>   -0.548</td> <td>    0.073</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L5.market_value</th> <td>   -0.4064</td> <td>    0.166</td> <td>   -2.454</td> <td> 0.014</td> <td>   -0.731</td> <td>   -0.082</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L6.market_value</th> <td>    0.1840</td> <td>    0.049</td> <td>    3.770</td> <td> 0.000</td> <td>    0.088</td> <td>    0.280</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.market_value</th> <td>   -0.9486</td> <td>    0.035</td> <td>  -27.053</td> <td> 0.000</td> <td>   -1.017</td> <td>   -0.880</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.market_value</th> <td>    0.7798</td> <td>    0.032</td> <td>   24.155</td> <td> 0.000</td> <td>    0.716</td> <td>    0.843</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.market_value</th> <td>   -0.5083</td> <td>    0.031</td> <td>  -16.321</td> <td> 0.000</td> <td>   -0.569</td> <td>   -0.447</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L4.market_value</th> <td>   -0.1562</td> <td>    0.159</td> <td>   -0.982</td> <td> 0.326</td> <td>   -0.468</td> <td>    0.156</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L5.market_value</th> <td>    0.0953</td> <td>    0.057</td> <td>    1.681</td> <td> 0.093</td> <td>   -0.016</td> <td>    0.206</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L6.market_value</th> <td>    0.0670</td> <td>    0.024</td> <td>    2.798</td> <td> 0.005</td> <td>    0.020</td> <td>    0.114</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           0.0857</td> <td>          -1.0503j</td> <td>           1.0537</td> <td>          -0.2370</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           0.0857</td> <td>          +1.0503j</td> <td>           1.0537</td> <td>           0.2370</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>          -2.0251</td> <td>          -0.0000j</td> <td>           2.0251</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.4</th> <td>           1.0011</td> <td>          -0.0000j</td> <td>           1.0011</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.5</th> <td>           1.5306</td> <td>          -0.2671j</td> <td>           1.5537</td> <td>          -0.0275</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.6</th> <td>           1.5306</td> <td>          +0.2671j</td> <td>           1.5537</td> <td>           0.0275</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           0.1028</td> <td>          -1.0612j</td> <td>           1.0662</td> <td>          -0.2346</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>           0.1028</td> <td>          +1.0612j</td> <td>           1.0662</td> <td>           0.2346</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>           1.3623</td> <td>          -0.2795j</td> <td>           1.3906</td> <td>          -0.0322</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.4</th> <td>           1.3623</td> <td>          +0.2795j</td> <td>           1.3906</td> <td>           0.0322</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.5</th> <td>          -2.1760</td> <td>          -1.4332j</td> <td>           2.6056</td> <td>          -0.4073</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.6</th> <td>          -2.1760</td> <td>          +1.4332j</td> <td>           2.6056</td> <td>           0.4073</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:           market_value   No. Observations:                 5021\n",
              "Model:                     ARMA(6, 6)   Log Likelihood              -27587.932\n",
              "Method:                       css-mle   S.D. of innovations             58.849\n",
              "Date:                Wed, 17 Jun 2020   AIC                          55203.864\n",
              "Time:                        03:14:15   BIC                          55295.164\n",
              "Sample:                    01-07-1994   HQIC                         55235.856\n",
              "                         - 04-05-2013                                         \n",
              "======================================================================================\n",
              "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
              "--------------------------------------------------------------------------------------\n",
              "const               5089.6477    568.179      8.958      0.000    3976.037    6203.259\n",
              "ar.L1.market_value     1.9275      0.032     59.960      0.000       1.864       1.990\n",
              "ar.L2.market_value    -1.7357      0.040    -43.372      0.000      -1.814      -1.657\n",
              "ar.L3.market_value     1.2673      0.034     36.745      0.000       1.200       1.335\n",
              "ar.L4.market_value    -0.2372      0.159     -1.496      0.135      -0.548       0.073\n",
              "ar.L5.market_value    -0.4064      0.166     -2.454      0.014      -0.731      -0.082\n",
              "ar.L6.market_value     0.1840      0.049      3.770      0.000       0.088       0.280\n",
              "ma.L1.market_value    -0.9486      0.035    -27.053      0.000      -1.017      -0.880\n",
              "ma.L2.market_value     0.7798      0.032     24.155      0.000       0.716       0.843\n",
              "ma.L3.market_value    -0.5083      0.031    -16.321      0.000      -0.569      -0.447\n",
              "ma.L4.market_value    -0.1562      0.159     -0.982      0.326      -0.468       0.156\n",
              "ma.L5.market_value     0.0953      0.057      1.681      0.093      -0.016       0.206\n",
              "ma.L6.market_value     0.0670      0.024      2.798      0.005       0.020       0.114\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            0.0857           -1.0503j            1.0537           -0.2370\n",
              "AR.2            0.0857           +1.0503j            1.0537            0.2370\n",
              "AR.3           -2.0251           -0.0000j            2.0251           -0.5000\n",
              "AR.4            1.0011           -0.0000j            1.0011           -0.0000\n",
              "AR.5            1.5306           -0.2671j            1.5537           -0.0275\n",
              "AR.6            1.5306           +0.2671j            1.5537            0.0275\n",
              "MA.1            0.1028           -1.0612j            1.0662           -0.2346\n",
              "MA.2            0.1028           +1.0612j            1.0662            0.2346\n",
              "MA.3            1.3623           -0.2795j            1.3906           -0.0322\n",
              "MA.4            1.3623           +0.2795j            1.3906            0.0322\n",
              "MA.5           -2.1760           -1.4332j            2.6056           -0.4073\n",
              "MA.6           -2.1760           +1.4332j            2.6056            0.4073\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RxXgi23rRQEg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 723
        },
        "outputId": "84c3670f-f797-4f77-8825-01695065e462"
      },
      "source": [
        "model_ar_5_ma_6 = ARMA(df.market_value, order=(5,6))\n",
        "results_ar_5_ma_6 = model_ar_5_ma_6.fit(start_ar_lags = 7)\n",
        "results_ar_5_ma_6.summary()"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(5, 6)</td>    <th>  Log Likelihood     </th> <td>-27587.863</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>58.849</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th>  <td>55201.726</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:14:38</td>     <th>  BIC                </th>  <td>55286.504</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55231.433</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5089.6468</td> <td>  580.990</td> <td>    8.760</td> <td> 0.000</td> <td> 3950.928</td> <td> 6228.366</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.market_value</th> <td>    1.3586</td> <td>    0.177</td> <td>    7.656</td> <td> 0.000</td> <td>    1.011</td> <td>    1.706</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.market_value</th> <td>   -1.1291</td> <td>    0.237</td> <td>   -4.761</td> <td> 0.000</td> <td>   -1.594</td> <td>   -0.664</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.market_value</th> <td>    0.9149</td> <td>    0.229</td> <td>    4.001</td> <td> 0.000</td> <td>    0.467</td> <td>    1.363</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L4.market_value</th> <td>    0.0157</td> <td>    0.204</td> <td>    0.077</td> <td> 0.938</td> <td>   -0.384</td> <td>    0.415</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L5.market_value</th> <td>   -0.1612</td> <td>    0.119</td> <td>   -1.352</td> <td> 0.176</td> <td>   -0.395</td> <td>    0.073</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.market_value</th> <td>   -0.3797</td> <td>    0.178</td> <td>   -2.134</td> <td> 0.033</td> <td>   -0.728</td> <td>   -0.031</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.market_value</th> <td>    0.7294</td> <td>    0.125</td> <td>    5.830</td> <td> 0.000</td> <td>    0.484</td> <td>    0.975</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.market_value</th> <td>   -0.2199</td> <td>    0.153</td> <td>   -1.438</td> <td> 0.150</td> <td>   -0.519</td> <td>    0.080</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L4.market_value</th> <td>   -0.1387</td> <td>    0.114</td> <td>   -1.215</td> <td> 0.224</td> <td>   -0.362</td> <td>    0.085</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L5.market_value</th> <td>   -0.0879</td> <td>    0.017</td> <td>   -5.325</td> <td> 0.000</td> <td>   -0.120</td> <td>   -0.056</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L6.market_value</th> <td>    0.0265</td> <td>    0.024</td> <td>    1.129</td> <td> 0.259</td> <td>   -0.020</td> <td>    0.073</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           0.0917</td> <td>          -1.0418j</td> <td>           1.0458</td> <td>          -0.2360</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           0.0917</td> <td>          +1.0418j</td> <td>           1.0458</td> <td>           0.2360</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>           1.0010</td> <td>          -0.0000j</td> <td>           1.0010</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.4</th> <td>           1.8978</td> <td>          -0.0000j</td> <td>           1.8978</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.5</th> <td>          -2.9847</td> <td>          -0.0000j</td> <td>           2.9847</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           0.1071</td> <td>          -1.0487j</td> <td>           1.0542</td> <td>          -0.2338</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>           0.1071</td> <td>          +1.0487j</td> <td>           1.0542</td> <td>           0.2338</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>          -1.5352</td> <td>          -1.5158j</td> <td>           2.1574</td> <td>          -0.3760</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.4</th> <td>          -1.5352</td> <td>          +1.5158j</td> <td>           2.1574</td> <td>           0.3760</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.5</th> <td>           1.5918</td> <td>          -0.0000j</td> <td>           1.5918</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.6</th> <td>           4.5767</td> <td>          -0.0000j</td> <td>           4.5767</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:           market_value   No. Observations:                 5021\n",
              "Model:                     ARMA(5, 6)   Log Likelihood              -27587.863\n",
              "Method:                       css-mle   S.D. of innovations             58.849\n",
              "Date:                Wed, 17 Jun 2020   AIC                          55201.726\n",
              "Time:                        03:14:38   BIC                          55286.504\n",
              "Sample:                    01-07-1994   HQIC                         55231.433\n",
              "                         - 04-05-2013                                         \n",
              "======================================================================================\n",
              "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
              "--------------------------------------------------------------------------------------\n",
              "const               5089.6468    580.990      8.760      0.000    3950.928    6228.366\n",
              "ar.L1.market_value     1.3586      0.177      7.656      0.000       1.011       1.706\n",
              "ar.L2.market_value    -1.1291      0.237     -4.761      0.000      -1.594      -0.664\n",
              "ar.L3.market_value     0.9149      0.229      4.001      0.000       0.467       1.363\n",
              "ar.L4.market_value     0.0157      0.204      0.077      0.938      -0.384       0.415\n",
              "ar.L5.market_value    -0.1612      0.119     -1.352      0.176      -0.395       0.073\n",
              "ma.L1.market_value    -0.3797      0.178     -2.134      0.033      -0.728      -0.031\n",
              "ma.L2.market_value     0.7294      0.125      5.830      0.000       0.484       0.975\n",
              "ma.L3.market_value    -0.2199      0.153     -1.438      0.150      -0.519       0.080\n",
              "ma.L4.market_value    -0.1387      0.114     -1.215      0.224      -0.362       0.085\n",
              "ma.L5.market_value    -0.0879      0.017     -5.325      0.000      -0.120      -0.056\n",
              "ma.L6.market_value     0.0265      0.024      1.129      0.259      -0.020       0.073\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            0.0917           -1.0418j            1.0458           -0.2360\n",
              "AR.2            0.0917           +1.0418j            1.0458            0.2360\n",
              "AR.3            1.0010           -0.0000j            1.0010           -0.0000\n",
              "AR.4            1.8978           -0.0000j            1.8978           -0.0000\n",
              "AR.5           -2.9847           -0.0000j            2.9847           -0.5000\n",
              "MA.1            0.1071           -1.0487j            1.0542           -0.2338\n",
              "MA.2            0.1071           +1.0487j            1.0542            0.2338\n",
              "MA.3           -1.5352           -1.5158j            2.1574           -0.3760\n",
              "MA.4           -1.5352           +1.5158j            2.1574            0.3760\n",
              "MA.5            1.5918           -0.0000j            1.5918           -0.0000\n",
              "MA.6            4.5767           -0.0000j            4.5767           -0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MSrvv03lRVS-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "8e7a22a1-5ff3-4a07-9fb0-38a38d4a5b04"
      },
      "source": [
        "model_ar_6_ma_1 = ARMA(df.market_value, order=(6,1))\n",
        "results_ar_6_ma_1 = model_ar_6_ma_1.fit(start_ar_lags = 7)\n",
        "results_ar_6_ma_1.summary()"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>   <td>market_value</td>   <th>  No. Observations:  </th>    <td>5021</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(6, 1)</td>    <th>  Log Likelihood     </th> <td>-27594.195</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>58.923</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Wed, 17 Jun 2020</td> <th>  AIC                </th>  <td>55206.389</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>03:14:55</td>     <th>  BIC                </th>  <td>55265.082</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-07-1994</td>    <th>  HQIC               </th>  <td>55226.956</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</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>const</th>              <td> 5089.6419</td> <td>  586.531</td> <td>    8.678</td> <td> 0.000</td> <td> 3940.063</td> <td> 6239.221</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.market_value</th> <td>    1.3921</td> <td>    0.058</td> <td>   23.934</td> <td> 0.000</td> <td>    1.278</td> <td>    1.506</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.market_value</th> <td>   -0.4369</td> <td>    0.059</td> <td>   -7.402</td> <td> 0.000</td> <td>   -0.553</td> <td>   -0.321</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.market_value</th> <td>   -0.0101</td> <td>    0.025</td> <td>   -0.409</td> <td> 0.683</td> <td>   -0.059</td> <td>    0.038</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L4.market_value</th> <td>    0.1126</td> <td>    0.025</td> <td>    4.527</td> <td> 0.000</td> <td>    0.064</td> <td>    0.161</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L5.market_value</th> <td>   -0.1158</td> <td>    0.025</td> <td>   -4.717</td> <td> 0.000</td> <td>   -0.164</td> <td>   -0.068</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L6.market_value</th> <td>    0.0573</td> <td>    0.014</td> <td>    4.067</td> <td> 0.000</td> <td>    0.030</td> <td>    0.085</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.market_value</th> <td>   -0.4127</td> <td>    0.060</td> <td>   -6.926</td> <td> 0.000</td> <td>   -0.529</td> <td>   -0.296</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.0010</td> <td>          -0.0000j</td> <td>           1.0010</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>          -1.7608</td> <td>          -0.0000j</td> <td>           1.7608</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>          -0.0803</td> <td>          -1.8407j</td> <td>           1.8425</td> <td>          -0.2569</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.4</th> <td>          -0.0803</td> <td>          +1.8407j</td> <td>           1.8425</td> <td>           0.2569</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.5</th> <td>           1.4694</td> <td>          -0.8691j</td> <td>           1.7072</td> <td>          -0.0850</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.6</th> <td>           1.4694</td> <td>          +0.8691j</td> <td>           1.7072</td> <td>           0.0850</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           2.4232</td> <td>          +0.0000j</td> <td>           2.4232</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:           market_value   No. Observations:                 5021\n",
              "Model:                     ARMA(6, 1)   Log Likelihood              -27594.195\n",
              "Method:                       css-mle   S.D. of innovations             58.923\n",
              "Date:                Wed, 17 Jun 2020   AIC                          55206.389\n",
              "Time:                        03:14:55   BIC                          55265.082\n",
              "Sample:                    01-07-1994   HQIC                         55226.956\n",
              "                         - 04-05-2013                                         \n",
              "======================================================================================\n",
              "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
              "--------------------------------------------------------------------------------------\n",
              "const               5089.6419    586.531      8.678      0.000    3940.063    6239.221\n",
              "ar.L1.market_value     1.3921      0.058     23.934      0.000       1.278       1.506\n",
              "ar.L2.market_value    -0.4369      0.059     -7.402      0.000      -0.553      -0.321\n",
              "ar.L3.market_value    -0.0101      0.025     -0.409      0.683      -0.059       0.038\n",
              "ar.L4.market_value     0.1126      0.025      4.527      0.000       0.064       0.161\n",
              "ar.L5.market_value    -0.1158      0.025     -4.717      0.000      -0.164      -0.068\n",
              "ar.L6.market_value     0.0573      0.014      4.067      0.000       0.030       0.085\n",
              "ma.L1.market_value    -0.4127      0.060     -6.926      0.000      -0.529      -0.296\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.0010           -0.0000j            1.0010           -0.0000\n",
              "AR.2           -1.7608           -0.0000j            1.7608           -0.5000\n",
              "AR.3           -0.0803           -1.8407j            1.8425           -0.2569\n",
              "AR.4           -0.0803           +1.8407j            1.8425            0.2569\n",
              "AR.5            1.4694           -0.8691j            1.7072           -0.0850\n",
              "AR.6            1.4694           +0.8691j            1.7072            0.0850\n",
              "MA.1            2.4232           +0.0000j            2.4232            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "819yhKZcRYGX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "ffa907af-ed1a-4c88-9fd2-00b1c82e1c96"
      },
      "source": [
        "print(\"ARMA(5,6):  \\t LL = \", results_ar_5_ma_6.llf, \"\\t AIC = \", results_ar_5_ma_6.aic)\n",
        "print(\"ARMA(6,1):  \\t LL = \", results_ar_6_ma_1.llf, \"\\t AIC = \", results_ar_6_ma_1.aic)"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARMA(5,6):  \t LL =  -27587.862947877395 \t AIC =  55201.72589575479\n",
            "ARMA(6,1):  \t LL =  -27594.194570986856 \t AIC =  55206.38914197371\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QvmhPnQSRZRz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "outputId": "97ea4a08-912a-4d0d-ea34-c7b577cc97ba"
      },
      "source": [
        "df['res_ar_5_ma_6'] = results_ar_5_ma_6.resid\n",
        "sgt.plot_acf(df.res_ar_5_ma_6, zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals of Prices\",size=20)\n",
        "plt.show()"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "psjtePQbRfFg",
        "colab_type": "text"
      },
      "source": [
        "### ARMA for Returns vs ARMA for Prices"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oc-sW48tRgCI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "062df15a-9b20-4277-d534-7abb200e5491"
      },
      "source": [
        "print(\"ARMA(5,6):  \\t LL = \", results_ar_5_ma_6.llf, \"\\t AIC = \", results_ar_5_ma_6.aic)\n",
        "print(\"ARMA(5,1):  \\t LL = \", results_ret_ar_5_ma_1.llf, \"\\t AIC = \", results_ret_ar_5_ma_1.aic)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARMA(5,6):  \t LL =  -27587.862947877395 \t AIC =  55201.72589575479\n",
            "ARMA(5,1):  \t LL =  -7889.311282945847 \t AIC =  15794.622565891694\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}