KF5 - GARCH(1,1) Analysis - Daily v3.ipynb

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   "source": [
    "# GARCH(1,1) model Python Code\n",
    "## Sector Volatility Prediction Performance using GARCH Models and Artificial Neural Networks\n",
    "## MSc Thesis\n",
    "## Curtis Nybo, 2020\n",
    "### Version: 3.0"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "My MSc Dissertation paper results for the GARCH section are derived using this notebook.\n",
    "\n",
    "I mainly utilize the works of Kenneth R. French for the datasets, Auquan, and Sarit Maitra."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "# Loading Required Libraries"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.dates as mdates\n",
    "from matplotlib.dates import DateFormatter\n",
    "formatter = DateFormatter('%Y')\n",
    "import os\n",
    "\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import skew\n",
    "from scipy.stats import kurtosis\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "from statsmodels.tsa.stattools import acf, pacf\n",
    "\n",
    "import datetime as dt\n",
    "import sys\n",
    "from arch import arch_model\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.tsa.api as smt\n",
    "import statsmodels.api as sm\n",
    "import scipy.stats as scs\n",
    "import statsmodels.stats as sms\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from arch.univariate import ARX\n",
    "\n",
    "import math\n",
    "from sklearn.metrics import mean_squared_error,r2_score,mean_absolute_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Controls (Choose the sector data and file location)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Sector to be analyzed - This value can be changed between Technology, Consumer Durables, Health, Manufacturing, Other.\n",
    "sector = 'Other'\n",
    "#Working Directory\n",
    "os.chdir('C:\\\\Users\\\\CurtisXPS\\\\OneDrive\\\\School\\\\MSc Finance\\\\Dissertation')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train and Test set criteria\n",
    "train_rng_start = 0 # These values are NOT dates, they are positions in the dataset index\n",
    "train_rng_end = 3086 # Range ends at but doesn't include this date (first date from test set)\n",
    "train_rng_len = 3086\n",
    "test_rng_len = 772\n",
    "test_rng_start = train_rng_end\n",
    "test_date_start = '2017-04-06'\n",
    "\n",
    "#Lags\n",
    "lag_ = 12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Crunching and cleaning the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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128.71547 \r\nL 100.229305 124.959689 \r\nL 100.392474 132.224161 \r\nL 100.446863 130.494525 \r\nL 100.501253 130.741616 \r\nL 100.555642 137.41307 \r\nL 100.610032 135.930525 \r\nL 100.7732 129.703834 \r\nL 100.82759 130.64278 \r\nL 100.881979 139.488634 \r\nL 100.936369 134.942161 \r\nL 100.990758 129.506161 \r\nL 101.208316 133.163107 \r\nL 101.317095 126.096307 \r\nL 101.371485 127.875361 \r\nL 101.589043 138.25318 \r\nL 101.697822 124.465507 \r\nL 101.91538 140.081652 \r\nL 102.078548 130.445107 \r\nL 102.350496 138.352016 \r\nL 102.459275 119.671943 \r\nL 102.513664 134.15147 \r\nL 102.676833 134.645652 \r\nL 102.785612 126.145725 \r\nL 102.840001 133.311361 \r\nL 102.894391 132.075907 \r\nL 103.057559 127.875361 \r\nL 103.111949 136.177616 \r\nL 103.166338 128.814307 \r\nL 103.220728 119.869616 \r\nL 103.275117 131.927652 \r\nL 103.438286 126.54107 \r\nL 103.547065 135.436343 \r\nL 103.601454 130.296852 \r\nL 103.655844 134.250307 \r\nL 103.819012 129.110816 \r\nL 103.873402 130.148598 \r\nL 103.982181 138.50027 \r\nL 104.03657 134.596234 \r\nL 104.254128 130.049761 \r\nL 104.308518 118.93067 \r\nL 104.362907 136.32587 \r\nL 104.417297 135.337507 \r\nL 104.580465 123.724234 \r\nL 104.743634 134.744489 \r\nL 104.798023 123.27947 \r\nL 105.015581 133.212525 \r\nL 105.069971 128.46838 \r\nL 105.12436 128.863725 \r\nL 105.17875 130.988707 \r\nL 105.396308 133.756125 \r\nL 105.450697 136.523543 \r\nL 105.505087 128.418961 \r\nL 105.559476 133.558452 \r\nL 105.722645 130.543943 \r\nL 105.777034 122.884125 \r\nL 105.831424 125.898634 \r\nL 105.940203 130.445107 \r\nL 106.103371 133.509034 \r\nL 106.26654 130.296852 \r\nL 106.320929 132.668925 \r\nL 106.484098 127.974198 \r\nL 106.538487 130.543943 \r\nL 106.592877 129.901507 \r\nL 106.647266 130.296852 \r\nL 106.701656 129.753252 \r\nL 106.919214 130.198016 \r\nL 106.973603 134.349143 \r\nL 107.027993 133.90438 \r\nL 107.082382 129.061398 \r\nL 107.245551 130.198016 \r\nL 107.29994 123.872489 \r\nL 107.35433 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115.023249 127.430598 \r\nL 115.077639 130.049761 \r\nL 115.240807 131.631143 \r\nL 115.349586 129.654416 \r\nL 115.458365 135.683434 \r\nL 115.621534 132.075907 \r\nL 115.730313 126.83758 \r\nL 115.784702 131.087543 \r\nL 115.839092 130.692198 \r\nL 116.05665 128.517798 \r\nL 116.219818 134.645652 \r\nL 116.382987 134.15147 \r\nL 116.437376 147.148452 \r\nL 116.491766 128.320125 \r\nL 116.546155 131.334634 \r\nL 116.600545 135.881107 \r\nL 116.763713 138.352016 \r\nL 116.818103 122.389943 \r\nL 116.872492 133.113689 \r\nL 116.926882 127.282343 \r\nL 116.981271 130.840452 \r\nL 117.14444 130.741616 \r\nL 117.198829 143.738598 \r\nL 117.307608 126.83758 \r\nL 117.361998 133.60787 \r\nL 117.633945 121.006234 \r\nL 117.688335 132.668925 \r\nL 117.742724 130.049761 \r\nL 117.905893 131.828816 \r\nL 118.014671 135.881107 \r\nL 118.069061 129.654416 \r\nL 118.12345 131.581725 \r\nL 118.286619 132.125325 \r\nL 118.341008 125.256198 \r\nL 118.395398 131.878234 \r\nL 118.449787 130.09918 \r\nL 118.667345 131.038125 \r\nL 118.721735 130.049761 \r\nL 118.776124 134.200889 \r\nL 118.884903 129.110816 \r\nL 119.048072 123.081798 \r\nL 119.21124 132.866598 \r\nL 119.26563 127.677689 \r\nL 119.428798 133.06427 \r\nL 119.483188 132.619507 \r\nL 119.537577 126.096307 \r\nL 119.591967 131.384052 \r\nL 119.646356 130.988707 \r\nL 119.809525 134.843325 \r\nL 119.918304 126.936416 \r\nL 119.972693 128.46838 \r\nL 120.027083 129.357907 \r\nL 120.190251 129.950925 \r\nL 120.244641 131.779398 \r\nL 120.29903 128.71547 \r\nL 120.35342 137.660161 \r\nL 120.407809 126.788161 \r\nL 120.570978 134.052634 \r\nL 120.625367 132.125325 \r\nL 120.679757 125.948052 \r\nL 120.734146 131.878234 \r\nL 120.788536 128.764889 \r\nL 120.951704 130.000343 \r\nL 121.006094 129.160234 \r\nL 121.114873 135.386925 \r\nL 121.169262 129.654416 \r\nL 121.38682 129.654416 \r\nL 121.44121 128.023616 \r\nL 121.495599 131.235798 \r\nL 121.549989 128.71547 \r\nL 121.713157 130.88987 \r\nL 121.876326 138.945034 \r\nL 121.930715 125.651543 \r\nL 122.093884 129.604998 \r\nL 122.148273 136.474125 \r\nL 122.202663 124.11958 \r\nL 122.257052 130.247434 \r\nL 122.311442 128.517798 \r\nL 122.47461 131.532307 \r\nL 122.529 128.418961 \r\nL 122.692168 137.808416 \r\nL 122.964116 127.529434 \r\nL 123.018505 130.791034 \r\nL 123.072895 133.509034 \r\nL 123.236063 125.948052 \r\nL 123.290453 128.369543 \r\nL 123.399232 131.482889 \r\nL 123.453621 128.863725 \r\nL 123.61679 131.680561 \r\nL 123.671179 140.229907 \r\nL 123.779958 121.895761 \r\nL 123.834348 129.703834 \r\nL 123.997516 131.97707 \r\nL 124.051906 130.000343 \r\nL 124.215074 138.203761 \r\nL 124.378243 130.148598 \r\nL 124.432632 142.799652 \r\nL 124.487022 129.01198 \r\nL 124.541411 142.898489 \r\nL 124.758969 126.145725 \r\nL 124.813359 137.758998 \r\nL 124.867748 130.741616 \r\nL 124.922138 128.46838 \r\nL 124.976527 147.099034 \r\nL 125.139696 115.224307 \r\nL 125.302864 146.555434 \r\nL 125.357254 131.384052 \r\nL 125.520422 133.014852 \r\nL 125.574812 141.613616 \r\nL 125.629201 137.41307 \r\nL 125.73798 115.273725 \r\nL 125.901149 132.916016 \r\nL 125.955538 128.71547 \r\nL 126.009928 125.404452 \r\nL 126.064317 133.261943 \r\nL 126.118707 126.738743 \r\nL 126.336265 144.47987 \r\nL 126.390654 122.19227 \r\nL 126.445044 135.386925 \r\nL 126.499433 124.514925 \r\nL 126.716991 125.75038 \r\nL 126.771381 138.50027 \r\nL 126.88016 138.450852 \r\nL 127.043328 132.026489 \r\nL 127.097718 124.860852 \r\nL 127.152107 131.43347 \r\nL 127.206497 125.355034 \r\nL 127.260886 130.692198 \r\nL 127.424055 134.546816 \r\nL 127.478444 112.110961 \r\nL 127.532834 128.814307 \r\nL 127.587223 137.067143 \r\nL 127.641613 129.703834 \r\nL 127.804781 135.979943 \r\nL 127.96795 127.529434 \r\nL 128.022339 133.261943 \r\nL 128.185508 121.747507 \r\nL 128.294287 133.410198 \r\nL 128.348676 130.247434 \r\nL 128.403066 124.514925 \r\nL 128.566234 133.212525 \r\nL 128.620624 126.738743 \r\nL 128.675013 133.261943 \r\nL 128.729403 132.866598 \r\nL 128.783792 130.445107 \r\nL 128.946961 138.203761 \r\nL 129.00135 137.462489 \r\nL 129.05574 130.148598 \r\nL 129.110129 134.596234 \r\nL 129.164519 143.837434 \r\nL 129.382077 126.639907 \r\nL 129.436466 134.102052 \r\nL 129.490856 133.36078 \r\nL 129.545245 122.142852 \r\nL 129.762803 134.052634 \r\nL 129.817193 125.602125 \r\nL 129.871582 148.58158 \r\nL 129.925972 135.090416 \r\nL 130.08914 136.227034 \r\nL 130.14353 124.267834 \r\nL 130.197919 149.66878 \r\nL 130.252309 128.221289 \r\nL 130.306698 133.06427 \r\nL 130.469867 132.866598 \r\nL 130.524256 112.802816 \r\nL 130.578646 133.459616 \r\nL 130.633035 142.157216 \r\nL 130.687425 132.075907 \r\nL 130.850593 143.343252 \r\nL 131.068151 119.919034 \r\nL 131.23132 144.825798 \r\nL 131.340099 111.32027 \r\nL 131.394488 133.706707 \r\nL 131.448878 121.747507 \r\nL 131.666436 137.462489 \r\nL 131.775215 119.77078 \r\nL 131.829604 132.767761 \r\nL 131.992773 124.514925 \r\nL 132.047162 149.075761 \r\nL 132.101552 133.509034 \r\nL 132.155941 132.224161 \r\nL 132.210331 138.994452 \r\nL 132.373499 137.758998 \r\nL 132.427889 129.25907 \r\nL 132.482278 131.631143 \r\nL 132.536668 131.384052 \r\nL 132.591057 121.500416 \r\nL 132.754226 124.811434 \r\nL 132.917394 140.328743 \r\nL 132.971784 131.581725 \r\nL 133.134952 130.445107 \r\nL 133.243731 141.020598 \r\nL 133.298121 132.916016 \r\nL 133.35251 144.875216 \r\nL 133.515679 130.09918 \r\nL 133.570068 144.77638 \r\nL 133.678847 121.549834 \r\nL 133.733237 136.128198 \r\nL 133.896405 126.886998 \r\nL 134.059574 149.12518 \r\nL 134.113963 134.15147 \r\nL 134.331521 126.788161 \r\nL 134.385911 108.503434 \r\nL 134.4403 126.985834 \r\nL 134.49469 139.785143 \r\nL 134.657858 117.695216 \r\nL 134.712248 125.009107 \r\nL 134.766637 134.793907 \r\nL 134.821027 119.869616 \r\nL 134.875416 122.093434 \r\nL 135.092974 147.444961 \r\nL 135.201753 125.602125 \r\nL 135.256143 137.314234 \r\nL 135.419311 134.892743 \r\nL 135.52809 126.046889 \r\nL 135.58248 139.290961 \r\nL 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166.693273 127.92478 \r\nL 166.747663 124.267834 \r\nL 166.802052 125.898634 \r\nL 166.856442 132.075907 \r\nL 167.01961 125.404452 \r\nL 167.074 127.974198 \r\nL 167.128389 117.349289 \r\nL 167.182779 133.60787 \r\nL 167.237168 131.828816 \r\nL 167.400337 133.509034 \r\nL 167.454726 124.020743 \r\nL 167.563505 139.538052 \r\nL 167.617895 136.968307 \r\nL 167.781063 118.535325 \r\nL 167.944232 147.593216 \r\nL 168.16179 119.177761 \r\nL 168.324958 128.46838 \r\nL 168.379348 127.92478 \r\nL 168.542516 128.418961 \r\nL 168.596906 133.90438 \r\nL 168.651295 117.250452 \r\nL 168.705685 132.224161 \r\nL 168.760074 140.328743 \r\nL 168.923243 128.764889 \r\nL 169.032022 138.747361 \r\nL 169.086411 122.044016 \r\nL 169.140801 138.994452 \r\nL 169.303969 140.625252 \r\nL 169.358359 134.596234 \r\nL 169.412748 144.529289 \r\nL 169.467138 115.570234 \r\nL 169.521527 149.273434 \r\nL 169.739085 125.75038 \r\nL 169.793475 134.250307 \r\nL 169.847864 119.820198 \r\nL 169.902254 128.764889 \r\nL 170.065422 117.645798 \r\nL 170.228591 138.747361 \r\nL 170.28298 130.494525 \r\nL 170.446149 123.773652 \r\nL 170.609317 139.192125 \r\nL 170.826875 124.11958 \r\nL 171.044433 141.910125 \r\nL 171.207602 124.514925 \r\nL 171.261991 128.073034 \r\nL 171.316381 130.692198 \r\nL 171.37077 139.34038 \r\nL 171.42516 124.218416 \r\nL 171.588328 135.090416 \r\nL 171.642718 134.99158 \r\nL 171.805886 128.221289 \r\nL 171.969054 125.849216 \r\nL 172.132223 138.25318 \r\nL 172.186612 126.689325 \r\nL 172.349781 126.145725 \r\nL 172.45856 130.741616 \r\nL 172.512949 128.764889 \r\nL 172.730507 132.668925 \r\nL 172.839286 131.285216 \r\nL 172.893676 133.953798 \r\nL 173.111234 121.352161 \r\nL 173.220013 130.000343 \r\nL 173.274402 122.637034 \r\nL 173.328792 129.55558 \r\nL 173.49196 130.692198 \r\nL 173.54635 137.116561 \r\nL 173.600739 126.442234 \r\nL 173.655129 128.863725 \r\nL 173.709518 138.648525 \r\nL 173.927076 125.45387 \r\nL 174.090245 142.750234 \r\nL 174.253413 129.901507 \r\nL 174.307803 136.86947 \r\nL 174.362192 122.686452 \r\nL 174.416582 134.497398 \r\nL 174.470971 134.546816 \r\nL 174.63414 124.168998 \r\nL 174.688529 125.849216 \r\nL 174.797308 148.532161 \r\nL 174.851698 127.727107 \r\nL 175.014866 137.511907 \r\nL 175.069256 125.256198 \r\nL 175.123645 129.209652 \r\nL 175.178035 126.29398 \r\nL 175.232424 132.421834 \r\nL 175.449982 120.956816 \r\nL 175.504372 129.407325 \r\nL 175.558761 128.913143 \r\nL 175.776319 126.985834 \r\nL 175.830709 138.203761 \r\nL 175.885098 125.058525 \r\nL 175.939488 131.43347 \r\nL 175.993877 128.46838 \r\nL 176.157046 127.38118 \r\nL 176.265825 129.80267 \r\nL 176.320214 128.517798 \r\nL 176.374604 121.994598 \r\nL 176.537772 130.692198 \r\nL 176.592162 129.950925 \r\nL 176.646551 127.035252 \r\nL 176.700941 127.92478 \r\nL 176.75533 130.939289 \r\nL 176.918499 131.18638 \r\nL 176.972888 124.860852 \r\nL 177.027278 127.677689 \r\nL 177.136057 133.756125 \r\nL 177.353615 127.480016 \r\nL 177.408004 132.421834 \r\nL 177.462394 131.235798 \r\nL 177.679952 128.320125 \r\nL 177.734341 132.570089 \r\nL 177.788731 131.581725 \r\nL 177.84312 126.936416 \r\nL 178.060678 126.046889 \r\nL 178.115068 127.825943 \r\nL 178.169457 133.90438 \r\nL 178.223847 127.677689 \r\nL 178.278236 129.55558 \r\nL 178.441405 129.160234 \r\nL 178.495794 130.64278 \r\nL 178.550184 121.450998 \r\nL 178.604573 130.988707 \r\nL 178.658963 143.985689 \r\nL 178.876521 125.849216 \r\nL 178.93091 132.718343 \r\nL 178.9853 127.677689 \r\nL 179.039689 127.875361 \r\nL 179.202858 136.029361 \r\nL 179.257247 145.171725 \r\nL 179.366026 121.203907 \r\nL 179.420416 142.404307 \r\nL 179.583584 123.526561 \r\nL 179.746753 148.729834 \r\nL 179.964311 104.54998 \r\nL 180.127479 137.907252 \r\nL 180.181869 143.194998 \r\nL 180.345037 130.64278 \r\nL 180.508206 153.819907 \r\nL 180.562595 118.68358 \r\nL 180.725764 141.811289 \r\nL 180.888932 111.567361 \r\nL 180.943322 139.538052 \r\nL 181.16088 142.05838 \r\nL 181.215269 116.706852 \r\nL 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228.534133 138.450852 \r\nL 228.697302 131.235798 \r\nL 228.751691 137.660161 \r\nL 228.806081 132.372416 \r\nL 228.86047 129.110816 \r\nL 228.91486 133.014852 \r\nL 229.186807 129.01198 \r\nL 229.241197 123.625398 \r\nL 229.295586 136.375289 \r\nL 229.513144 126.343398 \r\nL 229.567534 145.468234 \r\nL 229.621923 135.78227 \r\nL 229.676313 130.395689 \r\nL 229.839481 131.285216 \r\nL 229.94826 140.724089 \r\nL 230.057039 127.480016 \r\nL 230.220208 121.796925 \r\nL 230.328987 129.703834 \r\nL 230.437766 124.91027 \r\nL 230.655324 134.052634 \r\nL 230.764103 127.825943 \r\nL 230.818492 131.43347 \r\nL 230.981661 133.657289 \r\nL 231.09044 127.134089 \r\nL 231.199219 128.320125 \r\nL 231.362387 130.988707 \r\nL 231.416777 128.369543 \r\nL 231.471166 128.913143 \r\nL 231.525556 133.113689 \r\nL 231.579945 132.026489 \r\nL 231.743114 122.389943 \r\nL 231.797503 125.009107 \r\nL 231.960672 135.930525 \r\nL 232.12384 132.075907 \r\nL 232.232619 132.668925 \r\nL 232.287009 132.421834 \r\nL 232.341398 135.090416 \r\nL 232.613346 116.75627 \r\nL 232.667735 132.174743 \r\nL 232.722125 125.355034 \r\nL 232.885293 132.570089 \r\nL 232.939683 132.125325 \r\nL 233.048462 126.046889 \r\nL 233.102851 132.322998 \r\nL 233.26602 131.482889 \r\nL 233.320409 129.25907 \r\nL 233.374799 131.285216 \r\nL 233.483578 129.456743 \r\nL 233.701136 126.590489 \r\nL 233.755525 131.43347 \r\nL 233.809915 128.764889 \r\nL 233.864304 128.46838 \r\nL 234.027473 132.471252 \r\nL 234.081862 129.25907 \r\nL 234.136252 133.558452 \r\nL 234.190641 130.148598 \r\nL 234.245031 125.009107 \r\nL 234.408199 136.671798 \r\nL 234.462589 124.66318 \r\nL 234.516978 130.000343 \r\nL 234.571368 132.174743 \r\nL 234.625757 129.01198 \r\nL 234.788926 130.840452 \r\nL 234.843315 128.122452 \r\nL 234.897705 130.09918 \r\nL 234.952094 129.506161 \r\nL 235.006484 132.075907 \r\nL 235.224042 127.529434 \r\nL 235.278431 139.34038 \r\nL 235.332821 134.44798 \r\nL 235.38721 126.046889 \r\nL 235.550379 142.552561 \r\nL 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274.54765 125.45387 \r\nL 274.602039 130.296852 \r\nL 274.819597 129.110816 \r\nL 274.873987 132.767761 \r\nL 274.928376 131.136961 \r\nL 274.982766 127.183507 \r\nL 275.145934 132.075907 \r\nL 275.200324 128.270707 \r\nL 275.254713 130.791034 \r\nL 275.363492 133.60787 \r\nL 275.526661 126.788161 \r\nL 275.63544 133.657289 \r\nL 275.689829 129.703834 \r\nL 275.744219 134.69507 \r\nL 275.907387 128.863725 \r\nL 275.961777 140.97118 \r\nL 276.070556 121.500416 \r\nL 276.124945 134.250307 \r\nL 276.288114 125.305616 \r\nL 276.451282 133.854961 \r\nL 276.505672 126.83758 \r\nL 276.777619 138.895616 \r\nL 276.886398 130.543943 \r\nL 277.049567 124.613761 \r\nL 277.103956 134.15147 \r\nL 277.158346 132.27358 \r\nL 277.212735 129.209652 \r\nL 277.430293 130.840452 \r\nL 277.484683 132.372416 \r\nL 277.647851 127.974198 \r\nL 277.81102 131.482889 \r\nL 277.865409 131.235798 \r\nL 277.919799 129.160234 \r\nL 277.974188 130.445107 \r\nL 278.028578 137.314234 \r\nL 278.191746 127.825943 \r\nL 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "rawdata = pd.read_csv('Data\\\\Ken F - Five Sector\\\\' + sector + '.csv')\n",
    "rawdata['Date'] = pd.to_datetime(rawdata['Date'])\n",
    "rawdata = rawdata.set_index(['Date'])\n",
    "train_data = rawdata[train_rng_start:train_rng_end]\n",
    "test_data = rawdata[train_rng_end:]\n",
    "\n",
    "# Return Plot\n",
    "plt.plot(train_data, label='Training set')\n",
    "plt.plot(test_data, label='Test set')\n",
    "plt.title(sector + ' - Returns')\n",
    "plt.legend(loc='best')\n",
    "plt.ylim(-0.22, 0.22)\n",
    "plt.gcf().axes[0].xaxis.set_major_formatter(formatter)\n",
    "plt.ylabel('Return')\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_close_price.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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229.852912 \r\nL 101.528806 229.041238 \r\nL 101.691974 229.869094 \r\nL 101.746364 228.590431 \r\nL 101.800753 229.588152 \r\nL 101.855143 229.846306 \r\nL 101.909532 229.805684 \r\nL 102.072701 229.871736 \r\nL 102.12709 229.079108 \r\nL 102.18148 229.255248 \r\nL 102.290259 229.867443 \r\nL 102.453427 229.870525 \r\nL 102.507817 229.271651 \r\nL 102.562206 229.335061 \r\nL 102.670985 229.86348 \r\nL 102.834154 229.871736 \r\nL 102.888543 229.079108 \r\nL 102.942933 229.768695 \r\nL 102.997322 229.846306 \r\nL 103.051712 228.94271 \r\nL 103.21488 229.872727 \r\nL 103.26927 229.079108 \r\nL 103.323659 229.747228 \r\nL 103.378049 229.865572 \r\nL 103.595607 229.80007 \r\nL 103.649996 226.94958 \r\nL 103.704386 229.83882 \r\nL 103.813165 229.830454 \r\nL 103.976333 229.83882 \r\nL 104.139502 229.478174 \r\nL 104.35706 228.901757 \r\nL 104.465839 229.715523 \r\nL 104.520228 229.631306 \r\nL 104.574618 228.208978 \r\nL 104.846565 229.870525 \r\nL 104.900955 228.042526 \r\nL 104.955344 228.795523 \r\nL 105.172902 229.867443 \r\nL 105.227292 226.655426 \r\nL 105.281681 229.187434 \r\nL 105.336071 229.768695 \r\nL 105.553629 229.670937 \r\nL 105.608018 229.869094 \r\nL 105.662408 228.773616 \r\nL 105.716797 229.423571 \r\nL 105.934355 227.527868 \r\nL 106.097524 229.768695 \r\nL 106.260692 226.187776 \r\nL 106.369471 229.872727 \r\nL 106.423861 229.858636 \r\nL 106.47825 229.731816 \r\nL 106.695808 227.463137 \r\nL 106.750198 229.816252 \r\nL 106.804587 224.050871 \r\nL 106.858977 229.437552 \r\nL 107.022145 229.287833 \r\nL 107.076535 229.86348 \r\nL 107.130924 228.795523 \r\nL 107.185314 229.641544 \r\nL 107.239703 229.82594 \r\nL 107.402872 229.423571 \r\nL 107.457261 228.683785 \r\nL 107.511651 229.651562 \r\nL 107.56604 224.251671 \r\nL 107.62043 229.83882 \r\nL 107.783598 228.962856 \r\nL 107.892377 229.002487 \r\nL 107.946767 229.849719 \r\nL 108.001156 229.40937 \r\nL 108.218714 229.83882 \r\nL 108.327493 227.364388 \r\nL 108.381883 229.303796 \r\nL 108.545051 229.871736 \r\nL 108.599441 229.830454 \r\nL 108.65383 223.266499 \r\nL 108.70822 228.614099 \r\nL 108.762609 229.041238 \r\nL 108.925778 227.463137 \r\nL 108.980167 229.80007 \r\nL 109.034557 229.631306 \r\nL 109.088946 229.255248 \r\nL 109.143336 227.160947 \r\nL 109.306504 229.77541 \r\nL 109.360894 229.66136 \r\nL 109.415283 229.576813 \r\nL 109.469673 229.66136 \r\nL 109.524062 229.874379 \r\nL 109.74162 229.541475 \r\nL 109.79601 228.518103 \r\nL 109.850399 229.565253 \r\nL 109.904789 229.588152 \r\nL 110.067957 229.86348 \r\nL 110.122347 226.877362 \r\nL 110.176736 228.683785 \r\nL 110.285515 229.858636 \r\nL 110.448684 229.59927 \r\nL 110.611852 229.849719 \r\nL 110.82941 229.451313 \r\nL 110.992579 229.849719 \r\nL 111.046968 229.80007 \r\nL 111.264526 229.842673 \r\nL 111.318916 229.380307 \r\nL 111.373305 229.504155 \r\nL 111.427695 229.698349 \r\nL 111.590863 229.842673 \r\nL 111.645253 227.559903 \r\nL 111.699642 229.423571 \r\nL 111.754032 229.870525 \r\nL 111.808421 229.680295 \r\nL 112.025979 229.855884 \r\nL 112.080369 229.380307 \r\nL 112.134758 229.40937 \r\nL 112.189148 229.78818 \r\nL 112.352316 228.795523 \r\nL 112.461095 229.842673 \r\nL 112.569874 229.794235 \r\nL 112.733043 229.80007 \r\nL 112.787432 229.423571 \r\nL 112.841822 228.181787 \r\nL 112.950601 229.707046 \r\nL 113.168159 229.842673 \r\nL 113.276938 229.255248 \r\nL 113.331327 229.869094 \r\nL 113.712054 229.872727 \r\nL 113.875222 229.651562 \r\nL 113.929612 229.872727 \r\nL 113.984001 229.77541 \r\nL 114.09278 228.922344 \r\nL 114.310338 229.855884 \r\nL 114.364728 228.901757 \r\nL 114.419117 229.874379 \r\nL 114.473507 229.86348 \r\nL 114.636675 227.716778 \r\nL 114.691065 229.794235 \r\nL 114.745454 229.78818 \r\nL 114.799844 229.394948 \r\nL 114.854233 229.516815 \r\nL 115.017402 229.761759 \r\nL 115.071791 229.516815 \r\nL 115.126181 229.715523 \r\nL 115.18057 229.620848 \r\nL 115.23496 229.858636 \r\nL 115.452518 229.874048 \r\nL 115.615686 229.761759 \r\nL 115.778855 227.229642 \r\nL 115.833244 229.870525 \r\nL 115.942023 229.86348 \r\nL 115.996413 229.731816 \r\nL 116.159581 228.262701 \r\nL 116.26836 229.867443 \r\nL 116.32275 229.805684 \r\nL 116.377139 229.849719 \r\nL 116.540308 229.66136 \r\nL 116.649087 229.871736 \r\nL 116.703476 229.116097 \r\nL 116.757866 229.576813 \r\nL 117.029813 229.874048 \r\nL 117.138592 229.670937 \r\nL 117.35615 229.478174 \r\nL 117.41054 229.16993 \r\nL 117.464929 229.781905 \r\nL 117.519319 229.464854 \r\nL 117.845656 229.858636 \r\nL 117.900045 229.060283 \r\nL 118.117603 229.865572 \r\nL 118.171993 229.723779 \r\nL 118.226382 229.287833 \r\nL 118.280772 229.768695 \r\nL 118.552719 229.80007 \r\nL 118.607109 229.66136 \r\nL 118.661498 229.869094 \r\nL 118.879056 229.834747 \r\nL 118.987835 228.070819 \r\nL 119.042225 229.867443 \r\nL 119.205393 229.869094 \r\nL 119.314172 229.204718 \r\nL 119.368562 229.287833 \r\nL 119.422951 229.830454 \r\nL 119.694899 229.78818 \r\nL 119.749288 229.715523 \r\nL 119.803678 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126.874312 229.565253 \r\nL 126.928702 228.181787 \r\nL 126.983091 229.82594 \r\nL 127.037481 227.80826 \r\nL 127.255039 229.761759 \r\nL 127.309428 229.319539 \r\nL 127.363818 229.871736 \r\nL 127.418207 229.59927 \r\nL 127.581376 228.706573 \r\nL 127.744544 229.865572 \r\nL 127.798934 229.66136 \r\nL 127.962102 229.855884 \r\nL 128.016492 226.065909 \r\nL 128.125271 226.106751 \r\nL 128.17966 229.794235 \r\nL 128.397218 229.82594 \r\nL 128.451608 229.394948 \r\nL 128.505997 229.870525 \r\nL 128.560387 227.559903 \r\nL 128.723555 229.83882 \r\nL 128.886724 223.533461 \r\nL 128.941113 228.468784 \r\nL 129.104282 228.795523 \r\nL 129.158671 227.838314 \r\nL 129.213061 229.870525 \r\nL 129.26745 229.576813 \r\nL 129.32184 218.246519 \r\nL 129.485008 218.601551 \r\nL 129.539398 229.002487 \r\nL 129.593787 225.942061 \r\nL 129.648177 219.020323 \r\nL 129.702566 229.869094 \r\nL 129.865735 229.698349 \r\nL 129.920124 224.832931 \r\nL 129.974514 228.042526 \r\nL 130.083293 218.671897 \r\nL 130.246461 229.715523 \r\nL 130.300851 229.631306 \r\nL 130.35524 228.443794 \r\nL 130.40963 229.651562 \r\nL 130.627188 228.367504 \r\nL 130.681577 221.729791 \r\nL 130.735967 226.347182 \r\nL 130.790356 229.021973 \r\nL 130.844746 227.956328 \r\nL 131.062304 228.614099 \r\nL 131.116693 227.364388 \r\nL 131.171083 229.821206 \r\nL 131.225472 227.397525 \r\nL 131.388641 229.830454 \r\nL 131.44303 228.154375 \r\nL 131.49742 229.867443 \r\nL 131.551809 228.418584 \r\nL 131.606199 229.869094 \r\nL 131.769367 229.319539 \r\nL 131.823757 213.725895 \r\nL 131.878146 229.651562 \r\nL 131.932536 228.23595 \r\nL 131.986925 229.794235 \r\nL 132.150094 228.773616 \r\nL 132.204483 229.86348 \r\nL 132.258873 229.59927 \r\nL 132.313262 229.319539 \r\nL 132.367652 229.651562 \r\nL 132.53082 225.983564 \r\nL 132.693989 229.846306 \r\nL 132.748378 227.956328 \r\nL 132.911547 229.66136 \r\nL 132.965936 229.041238 \r\nL 133.020326 229.651562 \r\nL 133.129105 229.858636 \r\nL 133.292273 227.559903 \r\nL 133.346663 228.014014 \r\nL 133.401052 229.83882 \r\nL 133.455442 229.303796 \r\nL 133.509831 222.489724 \r\nL 133.781779 229.451313 \r\nL 133.836168 229.631306 \r\nL 133.890558 226.307661 \r\nL 134.053726 229.849719 \r\nL 134.108116 229.464854 \r\nL 134.162505 228.542432 \r\nL 134.216895 216.000739 \r\nL 134.271284 229.134262 \r\nL 134.434453 228.660776 \r\nL 134.488842 227.80826 \r\nL 134.543232 214.227893 \r\nL 134.652011 229.689432 \r\nL 134.815179 229.723779 \r\nL 134.869569 214.884894 \r\nL 134.923958 229.610169 \r\nL 134.978348 224.30132 \r\nL 135.032737 229.82594 \r\nL 135.195906 223.048967 \r\nL 135.250295 229.529255 \r\nL 135.304685 225.731244 \r\nL 135.576632 221.305184 \r\nL 135.631022 226.187776 \r\nL 135.685411 212.348483 \r\nL 135.739801 229.553474 \r\nL 135.79419 225.983564 \r\nL 135.957359 228.773616 \r\nL 136.011748 228.014014 \r\nL 136.120527 224.151711 \r\nL 136.174917 229.739632 \r\nL 136.338085 227.956328 \r\nL 136.392475 215.20811 \r\nL 136.501254 229.811078 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225.942061 \r\nL 191.597816 229.516815 \r\nL 191.652206 228.683785 \r\nL 191.706595 227.195404 \r\nL 191.760985 222.317657 \r\nL 192.032932 229.707046 \r\nL 192.087322 229.869094 \r\nL 192.30488 228.637548 \r\nL 192.359269 223.690996 \r\nL 192.413659 229.871736 \r\nL 192.468048 229.715523 \r\nL 192.522438 229.529255 \r\nL 192.685606 229.870525 \r\nL 192.903164 228.042526 \r\nL 193.066333 227.591719 \r\nL 193.120722 227.091372 \r\nL 193.229501 229.852912 \r\nL 193.283891 229.811078 \r\nL 193.501449 229.834747 \r\nL 193.555838 229.761759 \r\nL 193.610228 229.874048 \r\nL 193.827786 229.86348 \r\nL 193.882175 229.097713 \r\nL 193.936565 229.287833 \r\nL 193.990954 221.057708 \r\nL 194.045344 227.463137 \r\nL 194.208512 229.670937 \r\nL 194.262902 227.091372 \r\nL 194.317291 228.660776 \r\nL 194.371681 229.610169 \r\nL 194.42607 227.12627 \r\nL 194.589239 229.858636 \r\nL 194.643628 226.503066 \r\nL 194.698018 229.731816 \r\nL 194.752407 227.160947 \r\nL 194.806797 229.82594 \r\nL 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229.16993 \r\nL 215.529196 227.020916 \r\nL 215.583585 229.874379 \r\nL 215.637975 229.335061 \r\nL 215.692364 218.030858 \r\nL 215.746754 224.101401 \r\nL 215.909922 225.558627 \r\nL 216.073091 229.739632 \r\nL 216.12748 229.335061 \r\nL 216.290649 225.514922 \r\nL 216.345038 215.448211 \r\nL 216.399428 229.394948 \r\nL 216.508207 229.187434 \r\nL 216.725765 229.66136 \r\nL 216.780154 226.730286 \r\nL 216.834544 227.591719 \r\nL 216.888933 229.565253 \r\nL 217.106491 223.373945 \r\nL 217.160881 229.855884 \r\nL 217.26966 229.77541 \r\nL 217.432828 229.491275 \r\nL 217.487218 226.94958 \r\nL 217.541607 229.287833 \r\nL 217.595997 229.504155 \r\nL 217.650386 229.152206 \r\nL 217.867944 229.754604 \r\nL 217.922334 227.331032 \r\nL 217.976723 229.287833 \r\nL 218.031113 229.821206 \r\nL 218.248671 229.80007 \r\nL 218.30306 229.287833 \r\nL 218.35745 229.303796 \r\nL 218.411839 229.723779 \r\nL 218.575008 229.204718 \r\nL 218.629397 229.86348 \r\nL 218.792566 224.879939 \r\nL 219.010124 229.870525 \r\nL 219.064513 229.631306 \r\nL 219.118903 229.872727 \r\nL 219.173292 228.880951 \r\nL 219.44524 229.380307 \r\nL 219.499629 227.591719 \r\nL 219.554019 229.680295 \r\nL 219.771577 229.873498 \r\nL 219.880356 229.041238 \r\nL 219.934745 229.82594 \r\nL 220.097914 229.689432 \r\nL 220.152303 229.861168 \r\nL 220.261082 228.94271 \r\nL 220.315472 229.271651 \r\nL 220.47864 229.689432 \r\nL 220.53303 224.251671 \r\nL 220.587419 228.393154 \r\nL 220.641809 228.262701 \r\nL 220.696198 229.319539 \r\nL 220.859367 229.715523 \r\nL 220.913756 220.229081 \r\nL 220.968146 229.805684 \r\nL 221.022535 226.767385 \r\nL 221.076925 229.86348 \r\nL 221.240093 229.529255 \r\nL 221.348872 229.846306 \r\nL 221.403262 228.315543 \r\nL 221.457651 229.451313 \r\nL 221.62082 226.804264 \r\nL 221.729599 229.874048 \r\nL 221.783988 229.478174 \r\nL 221.838378 229.78818 \r\nL 222.001546 229.204718 \r\nL 222.055936 229.739632 \r\nL 222.110325 227.985281 \r\nL 222.164715 229.861168 \r\nL 222.382273 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225.808811 226.730286 \r\nL 225.91759 229.491275 \r\nL 226.026369 228.443794 \r\nL 226.189538 229.855884 \r\nL 226.298317 229.867443 \r\nL 226.352706 224.050871 \r\nL 226.407096 228.880951 \r\nL 226.570264 225.293096 \r\nL 226.733433 229.855884 \r\nL 226.787822 223.320332 \r\nL 226.950991 229.78818 \r\nL 227.00538 229.541475 \r\nL 227.168549 228.901757 \r\nL 227.331717 229.80007 \r\nL 227.494886 228.922344 \r\nL 227.549275 224.251671 \r\nL 227.821223 229.852912 \r\nL 227.875612 229.689432 \r\nL 227.930002 227.623314 \r\nL 228.201949 229.861168 \r\nL 228.310728 225.248071 \r\nL 228.473897 229.842673 \r\nL 228.528286 229.437552 \r\nL 228.637065 229.303796 \r\nL 228.691455 223.690996 \r\nL 228.963402 229.842673 \r\nL 229.072181 229.870525 \r\nL 229.289739 229.86348 \r\nL 229.398518 229.116097 \r\nL 229.452908 229.78818 \r\nL 229.724855 229.855884 \r\nL 229.779245 229.152206 \r\nL 229.833634 229.631306 \r\nL 230.051192 229.867443 \r\nL 230.105582 229.811078 \r\nL 230.159971 229.287833 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229.66136 \r\nL 251.698213 229.576813 \r\nL 251.752602 229.079108 \r\nL 251.806992 229.858636 \r\nL 251.861381 229.187434 \r\nL 251.915771 229.187434 \r\nL 252.133329 227.838314 \r\nL 252.187718 229.855884 \r\nL 252.242108 221.96758 \r\nL 252.296497 229.255248 \r\nL 252.459666 229.651562 \r\nL 252.514055 229.335061 \r\nL 252.568445 226.877362 \r\nL 252.622834 229.303796 \r\nL 252.840392 229.849719 \r\nL 252.894782 229.811078 \r\nL 252.949171 229.303796 \r\nL 253.003561 229.610169 \r\nL 253.05795 229.842673 \r\nL 253.221119 229.872727 \r\nL 253.384287 229.002487 \r\nL 253.438677 229.768695 \r\nL 253.710624 229.723779 \r\nL 253.819403 224.973293 \r\nL 253.982572 229.846306 \r\nL 254.036961 229.641544 \r\nL 254.091351 229.116097 \r\nL 254.14574 229.464854 \r\nL 254.363298 229.849719 \r\nL 254.472077 229.834747 \r\nL 254.526467 228.042526 \r\nL 254.580856 229.491275 \r\nL 254.798414 229.849719 \r\nL 254.852804 229.77541 \r\nL 255.124751 229.80007 \r\nL 255.179141 229.134262 \r\nL 255.23353 229.869094 \r\nL 255.28792 229.437552 \r\nL 255.342309 228.098891 \r\nL 255.559867 229.747228 \r\nL 255.614257 228.154375 \r\nL 255.668646 229.874379 \r\nL 255.723036 229.816252 \r\nL 255.886204 229.287833 \r\nL 255.940594 229.689432 \r\nL 255.994983 225.816231 \r\nL 256.049373 229.852912 \r\nL 256.103762 229.350363 \r\nL 256.266931 229.40937 \r\nL 256.430099 229.761759 \r\nL 256.484489 229.872727 \r\nL 256.647657 229.872727 \r\nL 256.810826 229.204718 \r\nL 256.865215 229.715523 \r\nL 257.191552 229.768695 \r\nL 257.245942 229.858636 \r\nL 257.40911 227.716778 \r\nL 257.572278 229.541475 \r\nL 257.626668 229.834747 \r\nL 257.898615 229.83882 \r\nL 257.953005 228.126743 \r\nL 258.007394 222.489724 \r\nL 258.170563 229.238624 \r\nL 258.224952 228.23595 \r\nL 258.279342 228.566542 \r\nL 258.333731 228.070819 \r\nL 258.388121 228.443794 \r\nL 258.551289 221.96758 \r\nL 258.660068 229.830454 \r\nL 258.714458 227.527868 \r\nL 258.768847 228.443794 \r\nL 258.932016 229.834747 \r\nL 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# Producing the variables we need\n",
    "\n",
    "train_data['Squared Return'] = train_data['Returns']**2\n",
    "train_sq_returns = train_data['Squared Return']\n",
    "train_returns = train_data['Returns']\n",
    "\n",
    "test_data['Squared Return'] = test_data['Returns']**2\n",
    "test_sq_returns = test_data['Squared Return']\n",
    "test_returns = test_data['Returns']\n",
    "\n",
    "plt.plot(train_sq_returns, label='Training set')\n",
    "plt.plot(test_sq_returns, label='Test set')\n",
    "plt.title(sector + ' - Squared Returns')\n",
    "plt.gcf().axes[0].xaxis.set_major_formatter(formatter)\n",
    "plt.legend(loc='best')\n",
    "#plt.ylim([-0.001,0.04])\n",
    "plt.ylabel('Squared Return')\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_log_returns.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Produce a histogram if needed\n",
    "\n",
    "# plt.hist(log_returns, bins=100)\n",
    "# plt.title(sector + ' Return Distribution')\n",
    "# plt.ylabel('Frequency')\n",
    "# plt.xlabel('Returns')\n",
    "# plt.savefig('Thesis Document\\\\Optimized GARCH Figures\\\\' + sector + '\\\\' + sector + '_return_dist.png')\n",
    "# plt.show()"
   ]
  },
  {
   "source": [
    "# Initial Descriptive Statistics for the datatset\n",
    "\n",
    "Uses JB stat, Q statistics, and ADF test. See paper for details. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "JB: 12562.42463 , 0.00000 | Q stat: 60.42908 , 1.8851e-08 | Q2 stat: 3355.47642 , 0.00000 | ADF: -11.01439 , 0.00000\n"
    }
   ],
   "source": [
    "desc_JB = sm.stats.stattools.jarque_bera(train_returns)\n",
    "desc_JB_s = desc_JB[0]\n",
    "desc_JB_p = desc_JB[1]\n",
    "\n",
    "desc_Q_f = sm.stats.acorr_ljungbox(train_returns, lags=[lag_], return_df=True)\n",
    "desc_Q_s = desc_Q_f.lb_stat.iloc[0]\n",
    "desc_Q_p = desc_Q_f.lb_pvalue.iloc[0]\n",
    "\n",
    "desc_Q2_f = sm.stats.acorr_ljungbox(train_sq_returns, lags=[lag_], return_df=True)\n",
    "desc_Q2_s = desc_Q2_f.lb_stat.iloc[0]\n",
    "desc_Q2_p = desc_Q2_f.lb_pvalue.iloc[0]\n",
    "\n",
    "desc_adf = sm.tsa.stattools.adfuller(train_returns)\n",
    "desc_adf_s = desc_adf[0]\n",
    "desc_adf_p = desc_adf[1]\n",
    "\n",
    "print ('JB: {:.5f} , {:.5f} | Q stat: {:.5f} , {:.5} | Q2 stat: {:.5f} , {:.5f} | ADF: {:.5f} , {:.5f}'.format(desc_JB_s, \n",
    "desc_JB_p, desc_Q_s, desc_Q_p, desc_Q2_s, desc_Q2_p, desc_adf_s, desc_adf_p))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Running the GARCH model with the found paramters from above cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "                     Constant Mean - GARCH Model Results                      \n==============================================================================\nDep. Variable:                Returns   R-squared:                      -0.001\nMean Model:             Constant Mean   Adj. R-squared:                 -0.001\nVol Model:                      GARCH   Log-Likelihood:                9403.41\nDistribution:                  Normal   AIC:                          -18798.8\nMethod:            Maximum Likelihood   BIC:                          -18774.7\n                                        No. Observations:                 3086\nDate:                Wed, Sep 30 2020   Df Residuals:                     3082\nTime:                        10:55:10   Df Model:                            4\n                                 Mean Model                                 \n============================================================================\n                 coef    std err          t      P>|t|      95.0% Conf. Int.\n----------------------------------------------------------------------------\nmu         7.4906e-04  1.697e-04      4.413  1.018e-05 [4.164e-04,1.082e-03]\n                              Volatility Model                              \n============================================================================\n                 coef    std err          t      P>|t|      95.0% Conf. Int.\n----------------------------------------------------------------------------\nomega      5.1806e-06  6.787e-14  7.633e+07      0.000 [5.181e-06,5.181e-06]\nalpha[1]       0.2000  1.700e-03    117.650      0.000     [  0.197,  0.203]\nbeta[1]        0.7800  7.430e-03    104.976      0.000     [  0.765,  0.795]\n============================================================================\n\nCovariance estimator: robust\n"
    }
   ],
   "source": [
    "# In this code for the GARCH(1,1) model, the p_ and q_ values both = 1\n",
    "p_ = 1\n",
    "o_ = 0 # This value stays as 0, unless using an EGARCH model\n",
    "q_ = 1\n",
    "\n",
    "# Using student T distribution usually provides better fit\n",
    "am = arch_model(train_returns, mean=\"Constant\", vol='GARCH', p=p_, o=o_, q=q_)\n",
    "res = am.fit(disp='off')\n",
    "#print(res.summary())\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Checking for white noise residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      lb_stat  lb_pvalue\n12  21.002609   0.050342",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>lb_stat</th>\n      <th>lb_pvalue</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>12</th>\n      <td>21.002609</td>\n      <td>0.050342</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "plot_acf(res.std_resid, lags=lag_, title=(\"{sector} GARCH({p_},{q_}) Resid ACF\".format(sector=sector, p_=p_, q_=q_)))\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_resid_acf.png')\n",
    "plot_pacf(res.std_resid, lags=lag_, title=(\"{sector} GARCH({p_},{q_}) Resid PACF\".format(sector=sector, p_=p_, q_=q_)))\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_resid_pacf.png')\n",
    "plt.show()\n",
    "plt.close()\n",
    "sm.stats.acorr_ljungbox(res.std_resid, lags=[lag_], return_df=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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R/wUZs0lLTeVthwAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      lb_stat  lb_pvalue\n12  21.691069   0.041132",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>lb_stat</th>\n      <th>lb_pvalue</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>12</th>\n      <td>21.691069</td>\n      <td>0.041132</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "plot_acf(res.std_resid**2, lags=lag_, title=(\"{sector} GARCH({p_},{q_}) Squared Resid ACF\".format(sector=sector, p_=p_, q_=q_)))\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_resid_2_acf.png')\n",
    "plot_pacf(res.std_resid**2, lags=lag_, title=(\"{sector} GARCH({p_},{q_}) Squared Resid PACF\".format(sector=sector, p_=p_, q_=q_)))\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_resid_2_pacf.png')\n",
    "plt.show()\n",
    "plt.close()\n",
    "sm.stats.acorr_ljungbox(res.std_resid**2, lags=[lag_], return_df=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forecasting using the above GARCH specification\n",
    "This section provides the forecast given the above specs that were used in the GARCH validation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reloading the test data and GARCH Model with above (p,q) specs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Weekly data from 01-02-2002 to 12-30-2019\n",
    "sector_data_fcst = pd.read_csv('Data\\\\Ken F - Five Sector\\\\' + sector + '.csv')\n",
    "sector_data_fcst['Date'] = pd.to_datetime(sector_data_fcst['Date'])\n",
    "\n",
    "sector_data_fcst = sector_data_fcst.set_index('Date')\n",
    "\n",
    "sector_data_fcst = sector_data_fcst[train_rng_start:] #Drop NA on the first line\n",
    "\n",
    "## Other Data Series Subsets\n",
    "log_returns_fcst = sector_data_fcst['Returns']\n",
    "sector_data_fcst['Squared Returns'] = sector_data_fcst['Returns']**2\n",
    "squared_log_returns_fcst = sector_data_fcst['Squared Returns']"
   ]
  },
  {
   "source": [
    "## Refitting the model"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "am_fcst = arch_model(log_returns_fcst, mean=\"Constant\", vol='GARCH', p=p_, o=o_, q=q_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Producing the rolling-window forecast for one week ahead with out-of-sample data\n",
    "\n",
    "Using the rolling window code from the ARCH library documentation (1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................\n                 h.1\n2017-04-05  0.000063\n2017-04-06  0.000059\n2017-04-07  0.000053\n2017-04-10  0.000047\n2017-04-11  0.000042\n...              ...\n2020-04-23  0.000597\n2020-04-24  0.000497\n2020-04-27  0.000734\n2020-04-28  0.000486\n2020-04-29  0.000623\n\n[772 rows x 1 columns]\n"
    }
   ],
   "source": [
    "## Rolling window forecast\n",
    "index = log_returns_fcst.index\n",
    "start_loc = 0\n",
    "end_loc = np.where(index >= test_date_start)[0].min()\n",
    "forecasts = {}\n",
    "for i in range(test_rng_len):\n",
    "    sys.stdout.write('.')\n",
    "    sys.stdout.flush()\n",
    "    res_fcst = am_fcst.fit(first_obs=i, last_obs=i + end_loc, disp='off')\n",
    "    temp = res_fcst.forecast(horizon=1).variance\n",
    "    fcast = temp.iloc[i + end_loc - 1]\n",
    "    forecasts[fcast.name] = fcast\n",
    "print()\n",
    "print(pd.DataFrame(forecasts).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "                 h.1\n2017-04-06  0.000063\n2017-04-07  0.000059\n2017-04-10  0.000053\n2017-04-11  0.000047\n2017-04-12  0.000042\n...              ...\n2020-04-24  0.000597\n2020-04-27  0.000497\n2020-04-28  0.000734\n2020-04-29  0.000486\n2020-04-30  0.000623\n\n[772 rows x 1 columns]\n"
    }
   ],
   "source": [
    "# Reformatting the data - The date shown in the above result is the final date used in the forecast\n",
    "# This cell pushes the date out one day to be plotted for the +1 day ahead forecast\n",
    "forecast_final = (pd.DataFrame(forecasts).T)\n",
    "forecast_final.index = forecast_final.index.shift(1, freq='B') \n",
    "print(forecast_final)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing the forecasted volatility values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(forecast_final)\n",
    "plt.gcf().axes[0].xaxis.set_major_formatter(formatter)\n",
    "plt.title(\"{sector} GARCH({p_},{q_}) Volatility Forecast\".format(sector=sector, p_=p_, q_=q_))\n",
    "plt.ylabel('Volatility')\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_vol_fcst_value.png')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## Overlaying the forecasted volatility values against the true squared returns in the out-of-sample data"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(squared_log_returns_fcst.iloc[(train_rng_len - 20):], label=\"True Squared Returns\")\n",
    "plt.plot(forecast_final, label=\"Forecast\")\n",
    "plt.gcf().axes[0].xaxis.set_major_formatter(formatter)\n",
    "plt.title(\"{sector} GARCH({p_},{q_}) Volatility Forecast vs Squared Returns\".format(sector=sector, p_=p_, q_=q_))\n",
    "plt.ylabel('Volatility')\n",
    "plt.legend(loc='best')\n",
    "#plt.savefig('Thesis Document\\\\KF5 Figures\\\\Optimized GARCH\\\\' + sector + '\\\\' + sector + '_full_volatility_fcst.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forecast Performance\n",
    "Producing the performance metrics (MAE, MAPE, RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0.0002379 MAE | \n0.0000009 MSE | \n0.0009354 RMSE | \n"
    }
   ],
   "source": [
    "test_set = pd.DataFrame(squared_log_returns_fcst[train_rng_len:])\n",
    "\n",
    "testMAE = mean_absolute_error(test_set, forecast_final)\n",
    "print('%.7f MAE | ' % (testMAE))\n",
    "\n",
    "testRMSE = math.sqrt(mean_squared_error(test_set, forecast_final))\n",
    "testMSE = testRMSE**2\n",
    "print('%.7f MSE | ' % (testMSE))\n",
    "print('%.7f RMSE | ' % (testRMSE))"
   ]
  },
  {
   "source": [
    "# References\n",
    "\n",
    "(1) Kevin Sheppard, Stanislav Khrapov, Gábor Lipták, mikedeltalima, Rob Capellini, esvhd, … jbrockmendel. (2019, November 22). bashtage/arch: Release 4.13 (Version 4.13). Zenodo. http://doi.org/10.5281/zenodo.3551028\n",
    "\n",
    "(2) Auquan - Time Series Analysis for Financial Data VI— GARCH model and predicting SPX returns - https://medium.com/auquan/time-series-analysis-for-finance-arch-garch-models-822f87f1d755 - 2017\n",
    "\n",
    "(3) Sarit Maitra - Forecasting using GARCH Processes & Monte-Carlo Simulations: statistical analysis & mathematical model using Python - https://towardsdatascience.com/garch-processes-monte-carlo-simulations-for-analytical-forecast-27edf77b2787 - 2019\n",
    "\n",
    "(4) Data Library - Kenneth R. French - https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html - 2020"
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
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