{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sunspots - ARIMA\n",
    "\n",
    "We will work on the [sunspot dataset](https://datamarket.com/data/set/22wg/wolfs-sunspot-numbers-1700-1988#!ds=22wg&display=line) and try to find the best ARIMA model.\n",
    "\n",
    "        SUNACTIVITY - Number of sunspots for each year\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.graphics.api import qqplot\n",
    "import seaborn as sns \n",
    "from pandas.tools.plotting import autocorrelation_plot\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "# df  = sm.datasets.sunspots.load()\n",
    "# dta = pd.DataFrame(df.data['SUNACTIVITY'],  index = sm.tsa.datetools.dates_from_range('1700', '2008'), columns = ['SUNACTIVITY'])\n",
    "# dta.plot()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zREly0yRqWBj8lWyg86dEg1nslgt7FsMLJp0wwGJ4NUhsEs2NYxYL5Oz2mvAM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\nzAJgLPComb1sZqlt9RTP/NM5nq8Dg6MY9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11445f470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load the data\n",
    "ts = pd.read_csv(\"../data/wolfs-sunspot.csv\", parse_dates = ['Year'], index_col = 'Year', infer_datetime_format = True)\n",
    "ts.columns = ['spots']\n",
    "ts.head()\n",
    "ts.plot(figsize=(12,6))\n",
    "ts.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Autocorrelation \n",
    "\n",
    "\n",
    "Using \n",
    "\n",
    "* sm.graphics.tsa.plot_acf\n",
    "* sm.graphics.tsa.plot_pacf\n",
    "* autocorrelation_plot\n",
    "\n",
    "Explore the autocorrelation of the **ts.spots**\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x119448748>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WPnK9eRWfz/9kHeFYku9+YiWSJLF1/yDf/cM20+svl1Q6zWd/tJZI\nPMU3br2Eaq+TZCrNZ364hlRa5Y6PXVoUcac3MDK7TvVmOCuXtPO+a7O37lfv2UjPUIgff/ryvN8O\n4NZvPU1rg5evvPcC49hdf9nFup29/M+HLy7yIcQSKW791tMsmlXPZ96+HICdh4f51m+3cN0ls7ih\n4Dd9Zms3//voHt57zQIuW6r9Pl0D43z5Z89zxbIO3vW6BXnjv/jT9YxHEnzvXy/LfucS9/PnfrKW\neDLNtz+2Mu+43uyr8J76n19vZu+xUX7ymSuKyut8/4FtvLhvkG9/7FLDBLd+Zy8//csubn71PK5e\nUWxl/9LdGxgMRPnhJ1dhkyRUVeUzP1pLMpXmOx9fmXe+VVXlCz9dz1gozvc+sRKnw04kluSLP11P\nJJ7k9lsvycvo10mm0nzrt1tQjo2yeHYDF53dyhObujjcG2ThzHpue8tSnA47/aMRvv27rfQNh4vu\nr1g8xa7DwyjHRpnV5ue6K+a9LM1hqyzLq2WNTv1fBa+z4iEgJsvyGuBbwCdlWb5ZluUPZBzdnwL+\nDqwB7i4nGHT06KNEns8hE61kUunUCGUtiFbSbaJWDmkozpIOZ3wOvkKfQya0VXdY6+ix94Xx/aWc\n0od6AlR5HMxoydcQVp3TQWuDj6df7DZqNeUST6TY1zXGjJbqvM/Tq80eNonASKbS9I9EaG/0FS0i\nna1+wrFkkX13OBijrtptWgm0wSTXwWjyY1GU0MwpPToeM3WOgnUtq7FMRnAhpXIdRk1s7bXVLuw2\nydIhHYunGBiNML25yjhnetmNckX79hwdZXQ8zsVntxm+E4fdxqVL2wlFk2wyyS3R7eKFkUq58y7y\nOYS081f4m4LeajX/XIxaOLBByy2prXLlXas9mbDd9ibrOeX6kXSHeX1NsfZa73czHknk3Z+lHOSN\nNR7GxuNFiXPDgSh2m1R0nbXUe1ExT8zrGQrjczvy7hc9S97M7xBPpOgZCjOjpdq4/iVJYt70WoLh\nRFH29vHBEP0jEZbMaTSEvtft4NqLZxJPpPnbhuIeMKl0ml88ugfl2CjnzW/mX9+ylEsWt/P5d5zL\n8nlN7D4ywjd/u4UHnznA1+7ZSN9wmGsumskNl83Oex+3y87y+c28/dXzuOjstqLPyaUS4XAh8DU0\nJ7JevvufFbzOFEVRVEVRblUU5dLMv72KovxGUZS7M88/oijKBYqirFAU5SeVvq/TJONZv1DMCu/Z\nbTYcdqkoz0Ff+K1CWbUx+QJFD+fzuQsd0uZlHYwwVl+hcDB38oWiCQZGo8xq8xfd2A67jVuumkda\nVfnlY3uKnNP7j4+RTKWNHbDOrMzFfshEOAyORUmlVdpMFh49cuNYjqNNz7w1c1yCeUkHvdNXYeir\nTmEJjWQqTSCcoN5koYKcSqs5wiSZSjMeSZgKoFIlNPTkq1znuk3SisKZJXJBtrjbtKas8Pb7XLTW\neznYHSgZNPB8JuTxwoX55cZ1Deh5k5BIPWKsraG4f7LLaafG58wTDnrOQmEdK53aaheBcDwvSmo4\nEKXG5zTNEwItXHVoLBve25OZU0dj8Zz0c5kbzjqUWZibTISDfl3kOlGtQnEhm0xauNgPBaLapqWg\ntLjulC5cuI2NUVP+xqi13ofLaTONWOoaCJFWVWa25Jvl9KqvhUX+9M59587PN1FevqyDumoX/9jc\nlZcMm0yl+dFDO1izo5eZbX7e/4aFRgtVl9POh9+0mGVnNbGva4yH1x4hmU7z3msW8OYr5ppuBCql\nkn4Os8uNmQw4TUJZS0UracftRZpDNlrJTHPQjkUq1Bysch2MMNbqyoTD0cwC3tlm3uN3yZxGLljY\nwvO7+9mwq4+Lc3YEermLRQWmo8ZaD9VeJ4dN6jnp8fOFIZIAM1qyEUvL5zcb3yetqpbCwayEhlFA\nzWRhgOwCoAuHMZOKr7mYtbsMhMyjc6B0ItzIeByf21HU66GxxsOeo6OmlX71cih6ATydudNqWbuj\nl57BUF7kl04imeYFZYB6v5t5BSWkW+t9tDb42GNS7rpn2Po3Au33PdavLVpaTkcCVTXfdYMmXFVV\nyyWprXajqipDgRjTm4sXep3mWi/7u8YYGovS2uCjZyiEZDGnOhPNwSwnQqchJz+mNfN+hkZnGlqb\nTSLViw/GEilGx+Ms6CwuzW1VAqRvJEJaVY330LHZJGa0VHOoO1hUr03XJvSNk45efn9f12ieqXPz\n3gHsNomlc/KFg9Nh581XzOXuh3fzi78pfPKt55BOq/z8r7t5cd8gC2fW87EblxRtXJ0OGx+/aQnH\n+scZHIuycGa9abTliVJJ4b1mWZbvl2V5UJblUVmWH5Rlubjz+ynGqJVkZlay2Pm4nLaiPIeoSblu\nHcOsVBCOF8mYjYo0B4uCcHo10ko1B323Mqst39may5svn4vdJvGn5w4ZsdWqqrJ57wAOu8T8Gfl2\ndUmSmNXuZ3AsWlSKOmuyKF4YZuqaQ44JS08maqo1X+j9VS6cDlteTPxwoDjEMBcjvDIjFKwysI3P\nyCS25QqHbGG/4t1ybQmz0kgwaoRH5pKtMFusPRzPKe6Wy9wypqUX9w0QjiW5cGGrqUnu7Fn1xOKp\nooqwvUNhaqtcRRsSnYYaD8lU2jBhljt/hcI1GNZyPayEN2RNLXrByO6hMI21HlMzbpXHgctpM2oj\ngXVOBGTDU4fNNAcT7cfs3tH/bjURVi0WZcd105iZ9tPZ6ietqkYhP52jmXsh1xcI2kbB63aw71jW\ngT4wGuFo3zgLZ9Wb/nYXn93G4jkN7Dw0zHd/v43bf/Mi63f2Maejhk/ctNRy0Zckic5WP+fOb54Q\nwQCVmZXuBDaiRSzNQivb/bMJ+fQJxGn4HEyS4Kw0B6e9KM8homsOZj4Ht4VZycrnkDErFfocCrOj\ndRprNJt9YWKRHu8+s9U6IqmpzsuqczroH4mwfqdmhjjQHaBnKMy585tNhZ0ubAr9Dj1D5slVoC0i\nNVWuPNur3jugo8l8l2mTJFrqvPSPRowkqKFAFHemab0Zurahl3kut7jZbFpiW65ZSRfCZq+x0hzC\n0SSRWMpUCzLMYyamJb10duE50HePVgmHT2/RosEuO6fd9HkjJ+VQtp92PJFiaCxqqTVAcWKYcf78\nZcxymfMxZJKcVsjcadr1s//4GMFwnEAobnkNSJJEW72P/pGwYWKzyokATSvRx+gMjkZxOmz4TYS9\nmXDQtYIWE83EMCuN5id09uiJhSYm1Zmt5n6Ho31B7DapSGu0ZfwO/aMR4/y/aJiUzCOlJEnig9ed\njTyjju0Hh9jfNca585v59NuWlexaeDKoRDjMURTlm5nEtFFFUW4HzPv3nUJ0B7OpWckkQxp0s5KF\nz8FE+nqtHNJRrcR34Wv0WkvFPgftcaFZyW6z0VjrLkrOOdI3jtftMN1h5XLNRTOxSRKPPX8UVVV5\ndmtm4VnaYTp+drt2sRealnqHw9qCbnJTgeavGArEjIWk22JhzKWl3kskljQS2YYDWoMXK5uocfNm\nbtasM9K6d3FdlZuxUNwQQGMlNAerEhr6oths0uFMXygHTZzSxwfGaahxF20QpjVXUVftYseh4aKs\n577hMLuPjCDPqDPV0gAWdNZjkyR2HckKh/6RCCrmzujCuQ4ZwlVvrGTl48m38ZvVPCpkZqsfh93G\ngeNjbM8UaTxrWq3l+NYGH/FkmpGAlindPxqhuc5reg20FvgEtPFhWuq8phqWbpoyFQ51xefJm3E4\nF2b76ybVjpLCId/f1tU/Tkem4msh8zKRcDsODqOqKhuVfiRg+VnWIdHVXieffvsyPnfLcv7zAxfy\n0RsWT5g2cCJUIhzU3AzpTKRSuSyNVxy9KmuugznrkDaXuG6n7QSjlaw1B4/bUXTRZjWHysxKoO2A\nAqE4scxn6Kn8M1uryzqXGms9rFjYwvGBEH9df4R1O3tpqvWwcFZx/DeYaw6qqtIzGKK5zmPZY1c3\nlRw8rqnLunAotVjlNmWJxJKEosmSC4/H5aDe7zZMVuU0B9CEbTyRNn4f/TVmTlibJOH3FZfQ0B2a\nZiayrGO9oKxHJMHoeLzIpATaTnDxnEbGI4mizPLHnteiUq481zx2HjRttLO1msM9QeNa7cqUoG6z\nECigaaGQFXajQetzAVmbvb6g6pFlpcxKDruNWe1+jvWPs26HlhNgtSOGrCbaOxxmPJIgGk/llfbO\npaHGg8MuGZuD8UiCSCxluUHye524XfY8rVu/dlotNjnTmqoYHIvmNZXqGQzjsNtM2592NFVht0l5\nmkPPcJh4Ml3kb9BZsaDFMPeu3dHLgeMBFs9pNPWD5eKw25A76+loqnpZTuWXQyXC4UvAOlmWH5Bl\n+UFgXebYpMJwSCfMfA7WZqVUWs0rplY6Wsm8VWg4mizyN0Bu2W6LaKVS6nFmkdIvxJkWzuhCXn9h\nJzZJ4oGnD5JMqdxy9XzTnRZo4YK11S4O5WgOA6MRQtFkyc+bk9kd7s+UhugeCtFY4zE9ZzqthgMw\nbOxKSy082mu8DAVixBMpY0dr5ZCGYtNIIGStOYC2UI6O59f7GTTpfKbTWLAb19HLZkyz0JyWZBrf\nb89pGDMSjLFmew8t9V7Ol1tMX6czf0YdqbRq/E56vaY57dY+KH3+unAwmhfVmwtww0Gb2XkPV2BW\nAjiroxZV1UqxtDX4SmqPuqmmdzicdUZbLPY2m0RznZe+kYihZWjzNB8vSRLNtV4GxrKmyz6TCrG5\n6MJc39ykVZWe4RBtDb6i6CbQ1hi9R7euBWad0eb3S0u9j6tXzGAoEOVnj+zWoguvnmc6drJRVjgo\nivIwsBz4OXAPsExRlEdO9sROFEmScDpsJFIn4HMwCX99qdFKZs4l3axUJBzCCao8DtOdeXtmd6U7\nfHVn9EyLi6+QzlY/n715Ga0NPq4+fwbLSqivALPbahgdjxuLr+44ndthbR6Y016DhLZIhaIJxsat\nbc06uZrDUBlntI7uSOwfiRiLlVUoK+Q4VTMag1UtIZ3GGg/xZDrP7GfWFjM7XnufwnBJ3d9gpjmA\n5lR2OWw8ubnL+KzfP7WfZErVTIEmC1EuumlCD4k8cHwMh11iZpu1D6rQrNQzFMLtsltqa7XVmaCB\nkXzh0FhCuwO4YnmHsclZsaC0kMvVHEo5o3Va632GKbKU/0Cnuc5DLJ4ynPD9IxHqql2WtnrdR6D/\nfsOBKPFEmg6TPA2dztZq4sm04Zs4kNGeZ5XYTF13ySwuX9aBPKOO1a+dbymgJxuVRCtdCfwxIxD2\nAhtkWb7kpM/sJeBy2ApKdus+B/OLQ7fj5foQjBahJq8xHNI50UppVSUaM9ccnA47LqeN8QKH9Nh4\nzFRrAIxwRn0h0MsEV6o5AMid9fzXBy/i5qvK71D07GDlmOYwPajvSqdZ70q9bgfTmqs43BMw7K+l\nbijIFw6VLjz6TdQ9FOJwb5C2Bp+liRCyiVb67n8sFMdhl6yd3ibVS806jek4HXYaazzGwqDTNZDf\nx7kQn8fJG1fOJhBO8ItH9/DEpmOs36VFoKxcYu6IziUbEjlGLJHiWP84M1v9Jc+F3+ukyuOga2Cc\nVDpN73CYDpOkRh2tR0M2aGAoEMNhl0ydv7m01Pv4xq0Xc9tblvKGTGUCK3KFg27bLyUccq+ZgQqE\ng76Z6B4MkUimGQ5EDY3IDF2Y6z2muwetAzF0Oguc0jsODuN1242kUjO8bgfvft0CPveOcy39f5OR\nSspnbAbepSjKjszjBcC9iqKseAXmVxF33PFtFWBNTyd2SeWiNq0Q1a7hZvoifi5uPYLHUVxNVRlt\nojtUwwUtx6hyaruNjf3TiCSdrOo4XDQ+kbbxXM8smjwhljT2WR7LZW1vJxIqF2fmlFbh6e451Lki\nLG8uTv5Oq/Bczyzc9iQXtnaxoW86sZSDy9oPczJMj8G4i00D02n3BVhQP8im/g7GE25WdRyi1IZ2\n32gDXaE6nLYkibSDxQ29NHut6+OrKjzdPZtqZ4w6d5Rj43Usb+qmzm1dAnsw4mP7cBut3iB9ET9t\nviAL68070QGMxDxsGeygs3qEubUjrO3tBFQuaTMvTHY0WMuBQGPe3Df2TyOc0H5/s/O9dbCN4ZiP\ny9oP4bBp987mgXYCcQ+XdRzGLpnfT2kVNg90EExoAskupTmv+bhx3ZVjQ990oikHi+r72THcxozq\nUc6qHS75Gn2uy5uO8+LgNNq8QRY2WJ+/bUOtDEWrWNl2mA39M3BIaeNemijW9HQiSeCyJRlPuLm0\n/QhOm3lZ6+MhP3tHm1lY389w1EtfxM9FrUfxOszL1PeHq9g50sqcmiHq3FE2D0xjWtUY8+vMux6m\n0hLP9Mymzh1heVMPhwJ1HA42sKShlyaLa3k05ubFwWnMqB6loyrAhr5Omj0hFpvc+6cDn/rUJ19W\n+QyPLhgAFEXZAxTHnk0CbJJKSs1+15RqM46b4ZC0izKZzp6GZNpmHC/Enjme+xn6ax0WF7hDSpFI\nZ3d4+t8uu3nLQZsEta4o4aSLYNxFOOmk2hk7KYIBoNoZxyGlGIl5SaUlxhNu/M5YScEAMMs/itOW\nIpF2UOeK0OSxFgwAkgQ+R5xQwsVgpAobafzO0iWEfQ5t4eyLaLu1WlfpLnlVmfHhpIuUKhFP2fFY\nnGcAT2aRiaaymkU06cDjSFqeb1/OZ4Am9EIJF15HwlIwgPa7Lm/uYZZ/hDZfkAtauioWDADtviBp\n1YYyqjl8a1zlyy/XZM5Xb1g7fz5n6b7GXrt2PoZjXhJpO/4KPuNEqXNHiaUcBBMeat1RS8GgzSdz\nrhNOIiknEipuu3X/Ev2cBOMexmKaEC51zdhtKh57glBCSwAMxD2Z97F+TbUzDqiMxrwMRzUNo6HM\ntX+6Ukl81B5Zlv8HuDfz+O1o5qVJw+rVWsO4vXdvYHQ8Zjy+43dbGDw4zDtvebep3fEvaw9z9JmD\nXPGqa1iccRpu/O6z+H1O4z0KWfONf1LX0Mbq1W8ANPVy/T0bWbxoIbdc9aai8T33bWbP0VFuvuV9\nOOw2DvcGWPu/m1h69gJuueqNpp/RsO4wDzx9kF5kIMT1r1rG5cuuPdHTUjHBh7bzgjJAzewrUXsO\ns2rFAm5cdU3Z1527b5AHnznArddfaBmKmUvtmkP88dlDRFI2ls5t5D1vKV0VMpVOs/8n6wwfxTtu\nvJbpLdZ2dlVV2fLdZ7H7mrn86st55hebOG/xXN75GvPvcrA7wM5fbmLO/OW8/dXziMSSPPXtZ1jQ\n2czqt77O9DVPvXice/+msPzCq7hkcTvDgSj//NFals1tY/UN5q+ZCGLxFP/2k7UEw1q46CduLi4Y\nV/IErckAABKdSURBVIhejLI3opk83nD1lSybZ+2DemLTMe57Yh/2+kUwMsSrL1luWmTu5XCoJ8D/\n/cUmAF63cimvWWF9XYeiCW773nNEXdOIRKN0NHt597usm0OqqsrOH6whaXNT21YDgQHe+/YbTP1H\nOvGHd7FmRy8Xv+rNbPzDNprrHLz/Pe8r+R2Cf9jGlv2DqPFqJBL8yy1vKus/Ox2pRHN4P1AF/Ab4\nRebvfzmZk3qpOB22ijvBQTajOZITfaT1j7aWmV63Pc9HEbbIjtbRI5b0ceUiaADOX9CC22mnayCE\n123nokWlC2S9XJZmBOPDaw8jAassErIKWTavia+9vzLBAOSV9TinjKMctLyPd+RUmi3n9JYkifbG\nKgZGIoajsJQjv7Gg8b3u9DTLcdDRAwb0REHdmWlWGmMicbvsvPt1C7hgYQufePPSsoIBstFMuuW4\nUr+QkbMw3Too4aUyu72GRbPqkSRKCirQQsGXzGmkbzhMIpnmokWlCzNIksTcjhpGgjE279VKkpQS\nDAAXZN7zL2sPE4ommVMiEEPnjStnAVp47Wsv7JySggEqq600kmm6cxFgB9YpijLxLYteBvfeezcA\nI8PtxJNefvnLu5EkiKeX4bBLRaGc+vjecDXQwpP/fIo9G4PcfMv7TFuE6uMBkrEZDEUl7r33blav\n/oARfVKV0yI0d3zPSBNQw333/4YPv+/dRphlrkM6d7yOXONl50gHVyybVqT1mI0HLLWdcuMvWdLG\n2h29KMdGWTK3kUf//OuS40/0/XWa67zIM+pQjo2wf8vf6dqRKjkeYNlZTczyD+O0pfn1r39Wdnx7\no4/9x8d45JltgJftm57g8La46Xi/z4nDbmPvoWPce+8GukN+oJnjh7Zw773PWr4/wPMv7iJ89CkO\nBeqBeg7uWgcrzcuQTeTvZZZHUGr8nI4aDnYHWLGghaaM89dq/E1veQ81PieBTLSPXgF4oq+3D79p\nMf0jESPHodT4Cxa2sGX/IJIElyxuLzt+TkcNL+7Tek3oUV6lxi+cWU+118mOg5r/Zk5HTdn5z2qr\n4cpzpzEajHHjqjkTfn5e6fFWlBUOsiy/Fi2MdT2apnGnLMvvz4S4Tip030IaCTtqUYGsQuwFPgd9\nd28V3QLgsKWIJbIL+3hU72ts7oZx2LQFMJH5jEo0B4BGT4Rvf3ylpUYykdhtNj70prO5/8n9vO6C\nTp55fONJ+6x/uW4Rv/7d700DBKyYXVNRvycgWw9qLO5FQqWqhJ3dJkk01rgZHtN+w/HM71rKF1JT\n5cIhpQgltd97JOYBVGpLONZPJZ966zISqXTZ6w20hLu3vXoed/1lF/V+t2US5Mul2uu0vF8KWTav\niRqfE7mz3rKwYy4rl7TTPRjiaP94Xm8VKxx2GyuXtPPY80dpqvVwzllN9O4uPy+r3ilTiUqilTYB\nb1EU5VDm8RzgQUVRlr0C86uIgYGgCvC9jC3w+7ddRpXHyed+spZkSuVbH73U9HWFzUN6hkL8+10b\nuHxZB+8uaD6i8637t7Dz0DA/+fTluJx2Hlmn+Qc++dZzjGSnXB7dcITfP3WAT9y0lGXzmrjvib08\nsamLL7/n/JKF9AQvDb0JDmi7/K//y0Ulx+uNkH786cv55m9e5HBvkB99alXJTYXeiOj/vGcF//nL\nTXS2+vnSu8+3HH86oaoqT2/pZla7f9Jcn5FYEqfDdtKEVTqtMh5N4Pc6T1k28qmiudn/sqKVnLpg\nAFAU5WCFr3vFKayvFImlTMtg6Hg9+RnPoYiuOVjvanStQi+mZ5iVLF5TXdDTIVsptPwuSHDiLOis\n46bL52C3SUbXuVLoWc37j49xLFMjp5RgALgg03fhV48rpNJqUa+M0xlJkrhi+bRJIxhAyxM4WYIB\ntGzsGp/rjBMM5ajEZnFUluXbyFZi/QBw5ORN6aVjNPzJCIdoPGXUjDFDL6Sn11bRTUR6BzczfB7d\nwZwwulVBNhu6EKOERua9Ryw6UwkmBkmSuPbiWbxmRSf2cvG4wJK5jTzxQhd/e/4o8WS6okz05fOa\ngd1GGQur2lUCwelMpdFKFwMHgUOZvydptFKmbHciRTKVzjiXrRd6vYqqLhxCZbQA7bl8zUHXNqxs\nqNnxmWqkwRj1/uLOVIKJxemwVXSOF3TW4XLasg7JEpnhOl63g5VL23HYbVx3ySwWTSHNQSDQqURz\nOEdRlLflHpBl+UbgwZMzpZeOK0dz0E1FJc1KRq2kjFmpAoe0XkMpnGNWskmSZUndaqPhT5JkKs1o\nMGZEUQhOPU6HnUUzG9iyf5DpzdVcuriyMN53v07mnVfPtyzNIhCc7liugrIsvw1wA1+TZfnLBa/5\nIpNQOOS2Cs1WV7W+eZ0OG3abZHR/q0xzyDcThaIJqrwOS3ulXvRtJBDVKoACDWVirwWvLFeeO42B\nsQgffOOiivIHQIvwOolmcIHglFNKc6gBLgH8wJU5x5PAv5/MSb1UXHnCQdccrL+ilNnx65qDEcpa\nIsxODy3N1RxKheXpYXu9w+Fsa0y/EA6TiSVzGk0jzQSCMxnLlVNRlLuAu2RZfrWiKP94Bef0ktF9\nDvFkKiscTEpv5+Jx2bM+B90hXcKslOtDUFWVUCRp2qM2l7YGHwe7A0YGbrlqpAKBQHCqqcTn8B+y\nLBdpCoqivOokzOdlkWdWilk37cnF63YYteWz0UolNAdPthxGJJYkrapGuKoVbZms3T1HtbLYUzXd\nXiAQTB0qEQ5fyfnbCbwJMO+WforJMytJ5R3SoAmHaDxFOqMFOOw2y85xkB+tlA1jLS0c9JILOw9r\nETFCOAgEgslOJbWVni449IQsyxuAL5uNP5XoBfbiyTTpTOZ3WeGQeT4WT5V1LkN+nsN4mTBWHb15\niN7wXpiVBALBZKeS2kqdOQ8lYDEwKb13bkd2oU/atQXeW4FZCbRch1AkUbKBPWg+DEmCUCyZU3Sv\n9GfkVi2trXZZhr0KBALBZKGSVSpXc0gDg8A3T850Xh5GDkIsYTiny2kOnpzoo3A0adkkXscmSfjc\nDsLRZDb0tYzm0JQTuvovb1gk0vQFAsGkpxKz0mwAWZadwE3Ah9CEw09O7tROHN28E4ok8bh1s1Lp\nr6iHpg6MRVApv9CDlusQiiYYDWmhqbW+0qUwHHYbH7l+MR63nUWzGsq+v0AgEJxqKjErzUYTCO8B\n6oGvA289udN6aVR5c4rcZTbn5TQHvfbSwW6tTo6vRBirjs/jYGQwRt9wpul5mVBW0Br4CAQCwelC\nqQzpG4APA+cCDwGrgbsURfnaKzS3EyY3e9mR8TmUy3PQ/QG7j2gBWH5v+YJ4NVUuDvcGOXB8DAlo\nKVHcTyAQCE5HShUAeAAYBS5WFOWDiqI8juZzmLQ4HTbcTjuhSLKiDGnItp7UNYfO1vLtHvUxxwdD\nNNZ6ypZ4FggEgtONUivnUjRT0nOyLB9G6yE96cNsqrwOxiMJwzxUzqxU7XXi9zkJZlojzplWvihe\nblnn1nrrfsMCgUBwumKpOSiKskNRlM8A04D/Aq4AWmVZfkSW5WteofmdMLqzOBrXEtoqaRKim5b8\nPifNFRTFyxMOFfgbBAKB4HSj7MqpKEpKUZQ/KYpyAzAd+AeasJiUVHm0jOdQJFlWa9DRTUtzO2or\nCjNtrPUYmdKt9UI4CASCqccJmYkURRkA7sj8m5To4axDgWhFDckhW95idkdlrRElSWJmm59dh0eE\n5iAQCKYkk96HcKLo4ayptFrWGa1z0aJWjg+EWLW0skYvoLWKPNo3zqz28m0lBQKB4HRj6gmHnAqp\nleQsAPh9Lt7z+gUn9DmvPu//t3evMXLVZRzHv2vbRYVt8UVtYtBooDwYwkXWS4SGaqgCTYziJSQa\nA9RIUu9rwEQRjUTURI1NedHES7Eo8YJGSEqgGCFmWxUJ4KWRPJRojG+IWIXdpdpSWV+cszCd/2zd\ndnfncvb7eXVmzkz2/+S/md+cc+Y8/1O4aPSUY3qPJA2Kxq1l1doEby6LxUuSSo0Lh9aFek6dw2Lx\nkqRS88Kh5cjhtDncsyBJKjUvHFqOHFxUR5KOT+PCwbUSJGn+GvdJ+oo1I1xxSfBqW2NL0nEbmq6X\n0xxkTzwxOfhFSFKXrV49MmtLiMadVpIkzZ/hIEkqGA6SpILhIEkqdP3XShHxQuD7wEuBCeCKzNzf\n9potwAXAZP3U2zNzEklSV/Tip6ybgT9k5g0RcTlwPfCJtteMAhdn5j+7PjpJUk9OK60D7q637wI2\ntO6MiCFgLfDNiNgdEVd1eXyStOQt6pFDRGwCxoCZ+xCGgMeBp+rHk0B7d7wTga1UCwotB+6LiAcy\nc+9ijlWS9LxFDYfM3A5sb30uIn4KzPTSHgGebHvbAWBrZv6nfv29wDmA4SBJXdKL00p7gI319kZg\nvG3/6cCeiBiKiBVUp6Ee6uL4JGnJ68UF6W3AjogYBw4C7wWIiDFgX2bujIhbgPuBQ8COzHykB+OU\npCXL3kqStETZW0mSdEwMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQ\nJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUM\nB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lS\nwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBUMB0lSwXCQJBWW9+oPR8Rl\nwLsz830d9n0QuBp4BrgxM+/s9vgkaSnryZFDRGwBbgSGOuxbA3wUeCNwCfDliFjR3RFK0tLWq9NK\ne4DNs+x7PbA7Mw9n5gSwDzi7ayOTJC3uaaWI2ASMAdNURwnTwFWZeVtErJ/lbSuBp1oeTwGrFnOc\nkqQjLWo4ZOZ2YPsxvm2CKiBmjABPLtigJEn/V88uSB/Fb4EvRsQw8CLgDGDv0d6wevVIce1CknT8\n+iYcImIM2JeZOyNiK7Cb6lTUZzLzUG9HJ0lLy9D09HSvxyBJ6jPeBCdJKhgOkqSC4SBJKhgOkqRC\n3/xaSUeKiAd5/mbAvwBfAr4LPAvszcwP92hoCyIi3gB8JTPfHBGn0qG2JvTYaqvzXGAn8Gi9e1t9\nQ+jA1hkRy6nuZXolMEzVFudPNGw+Z6nzbzRsPlv5a6U+FBEnAL/KzNGW5+4AvpaZ4xGxDbg7M+/o\n2SDnISKuBd4PTGXm+Z1qA34D/Bw4D3gx1U+bRzPzmV6N+1h1qPMDwMrM/EbLa9YwwHVGxJXA2Zn5\nyYg4Gfg98DsaNp9tdb6EqsYvAKuaNJ+tPHLoT+cAJ0bELmAZcB1wXmaO1/vvAt4CDGQ4AI8BlwHf\nqx+PttX2Vqpvnbsz8zAwEREzPbYe7PZg56GoEzg9It5B9W1zjJZeYgxmnT8Gbqu3lwGHKf9XmzCf\nrXW+gOqoYBQ4o2Hz+RyvOfSnA8BXM/NiqgaFt3JkB9tJBrjfVGb+jOpDZEZ7bSup2qYMdI+tDnXe\nD1ybmeuBPwOfZ8B7iWXmgcx8OiJGqD48r6OB89mhzs9SdXO4pknz2cpw6E+PUgUCmbkP2A+sadnf\ntH5Tz7Zsz9TWxB5bt2fmwzPbwLlUHyQDXWdEvBy4F9iRmT+kofPZoc5GzucMw6E/bQK+DhARL6P6\nZ7unpZPtpcD4LO8dRA9FxIX19kxtDwDrImI4IlYxhx5bA2BXRLy23r6I6lTDQNdZn2PfBXwqM3fU\nTz/ctPmcpc7GzWcrrzn0p+8AN0fEONW3sCupjh6+XS989Ajwk94Nb8FdA3yrtbbMnG5gj63NwE0R\ncQh4HLg6M6cGvM5PAycD10fE56ja8n+cqs4mzWenOseALQ2bz+f4ayVJUsHTSpKkguEgSSoYDpKk\nguEgSSoYDpKkguEgSSoYDtI8RMT6iLiv1+OQFprhIM2fNwupcbxDWlpgEbEM2AacSdUTK4F3ZubB\niPgY8BHgX/Xzj2XmDT0brDQLjxykhXc+cDAzLwDWUvX13xgRZ1G10HgNcGG9T+pLHjlIC6xe5GZ/\nRHyIqvHaacBJwAZgZ2Y+DRARP6Dq1yP1HY8cpAUWEW+jark+RbW05DhVE7b/Ui2II/U9w0Gav6G2\nxxuAH2XmLcDfqU4hLQN+AVwaESdFxDDwLryYrT7laSVp/tZFxARVSExTrfj2poh4D3AQ+DXwqsy8\nOSJuqh9PAf8A/t2jMUtHZThI85CZvwRWzOW1EbEWGM7Ms+rHt1OtdyD1HcNB6p6/Aq+LiD9SLeK0\nKzPv7PGYpI5c7EeSVPCCtCSpYDhIkgqGgySpYDhIkgqGgySpYDhIkgr/A17w/PeWUGVPAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114497dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "autocorrelation_plot(ts.spots)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a5d7ac8>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a5d7ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.graphics.tsa.plot_pacf(ts.spots, lags = 40 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train a ARMA(2,0)\n",
    "\n",
    "arma = sm.tsa.ARMA(dta, (2,0)).fit()\n",
    "\n",
    "Look at the params and different model section metrics: AIC, BIC, HQIC\n",
    "\n",
    "* print(arma.params)\n",
    "* print(arma.aic)\n",
    "* print(arma.bic)\n",
    "* print(arma.hqic)\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "arma = sm.tsa.ARMA(ts.spots.values, (2,0)).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 49.12845248   1.38862902  -0.69062875]\n",
      "2452.3812325756367\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11b808c88>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TbSFnQtOSN/jhjH5sRm7wf1beIcXQWE2fY/quR5n+eFh7y/E8lCR5GVFEDs/0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\nEAQtIop+EARBi/gHbKrm4iV7YwsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11abb5160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(arma.params)\n",
    "print(arma.aic)\n",
    "plt.plot(arma.resid)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Residuals\n",
    "\n",
    "Residuals are available via: arma.resid\n",
    "\n",
    "* QQ plot\n",
    "* Autocorrelation and Partial ACF \n",
    "* Normality and correlation tests\n",
    "\n",
    "\n",
    "Conclusion?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Sa7tx2VDgCSdndgrcaec8VC+pL9kE6HgQBGPp2fQkCIK9gI68ViVJUpHLdWOU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b849390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "fig = qqplot(arma.resid, line='q', ax=ax, fit=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tP5o0AOufvptsNsPiVashlzusbr/5Xddhy//md12qK9EbT3WIRzWLJ029hjswJA34JcBl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118943160>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tP5o0AOufvptsNsPiVashlzusbr/5Xddhy//md12qK9EbT3WIRzWLJ029hjswJA34JcBl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118943160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.graphics.tsa.plot_pacf(arma.resid, lags = 40 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0791846950150599"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.stats.durbin_watson(arma.resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NormaltestResult(statistic=42.740172867251623, pvalue=5.237082122131442e-10)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.normaltest(arma.resid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction\n",
    "\n",
    "To predict a slice of the time series:\n",
    "\n",
    "        y_hat = arma.predict('1990', '2012', dynamic=True)\n",
    "\n",
    "To plot: \n",
    "\n",
    "        ax = ts.spots.ix['1950':].plot(figsize=(12,8))\n",
    "        ax = y_hat.plot(ax=ax, style='r--', label='Dynamic Prediction');\n",
    "        ax.legend();\n",
    "        ax.axis((-20.0, 38.0, -4.0, 200.0));\n",
    "\n",
    "### Score\n",
    "\n",
    "* Mean Square Error\n",
    "* Mean Forecast Error \n",
    "\n",
    "        def mean_forecast_err(y, yhat):\n",
    "            return y.sub(yhat).mean()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Found arrays with inconsistent numbers of samples: [ 289 1722]",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-50-2db3250a31f5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmetrics\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmean_squared_error\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mmse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_hat\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mspots\u001b[0m \u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Users/aperrier/anaconda/envs/py35/lib/python3.5/site-packages/sklearn/metrics/regression.py\u001b[0m in \u001b[0;36mmean_squared_error\u001b[0;34m(y_true, y_pred, sample_weight, multioutput)\u001b[0m\n\u001b[1;32m    229\u001b[0m     \"\"\"\n\u001b[1;32m    230\u001b[0m     y_type, y_true, y_pred, multioutput = _check_reg_targets(\n\u001b[0;32m--> 231\u001b[0;31m         y_true, y_pred, multioutput)\n\u001b[0m\u001b[1;32m    232\u001b[0m     output_errors = np.average((y_true - y_pred) ** 2, axis=0,\n\u001b[1;32m    233\u001b[0m                                weights=sample_weight)\n",
      "\u001b[0;32m/Users/aperrier/anaconda/envs/py35/lib/python3.5/site-packages/sklearn/metrics/regression.py\u001b[0m in \u001b[0;36m_check_reg_targets\u001b[0;34m(y_true, y_pred, multioutput)\u001b[0m\n\u001b[1;32m     72\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     73\u001b[0m     \"\"\"\n\u001b[0;32m---> 74\u001b[0;31m     \u001b[0mcheck_consistent_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     75\u001b[0m     \u001b[0my_true\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mensure_2d\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     76\u001b[0m     \u001b[0my_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_pred\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mensure_2d\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/aperrier/anaconda/envs/py35/lib/python3.5/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_consistent_length\u001b[0;34m(*arrays)\u001b[0m\n\u001b[1;32m    174\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0muniques\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    175\u001b[0m         raise ValueError(\"Found arrays with inconsistent numbers of samples: \"\n\u001b[0;32m--> 176\u001b[0;31m                          \"%s\" % str(uniques))\n\u001b[0m\u001b[1;32m    177\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    178\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Found arrays with inconsistent numbers of samples: [ 289 1722]"
     ]
    },
    {
     "data": {
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6SEsleD0CYmFfV//8UCKEUEDEOCvDRESmYhgmItJBWiohEQvA0+HCDY1HELBycQwTU3nk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\nEEIIMWVJMCyEEEIIIaas/x+fImAp3zVn8gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c6a8f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_hat = arma.predict(start=1990, end=2010, exog=None,  dynamic=False)\n",
    "\n",
    "ax = ts.spots.ix['1950':].plot(figsize=(12,8))\n",
    "plt.plot(y_hat, 'r--', label='Dynamic Prediction');\n",
    "ax.legend();\n",
    "ax.axis((-20.0, 38.0, -4.0, 200.0));\n",
    "\n",
    "from sklearn.metrics import mean_squared_error as mse\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Grid Search\n",
    "\n",
    "Loop over p, d, q to find the best model according to AIC or MSE\n",
    "\n",
    "Look at the \n",
    "\n",
    "* Durbin Watson score and normality test to validate the normality of residuals\n",
    "* AIC to select the best model\n",
    "* MSE to select the best prediction\n",
    "\n",
    "\n"
   ]
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