ARMA-2007-2009 3M.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.read_excel('libor 3month version to use.xls',sheetname='data to use',index_col='Date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_forecast = df.loc['20090101':'20091231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "253"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_forecast)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.loc['20070101':'20081231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.to_excel('Results/in-sample.xls')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stationary Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.tsa.stattools import adfuller\n",
    "def test_stationarity(timeseries):\n",
    "    \n",
    "    #Determing rolling statistics\n",
    "    rolmean = pd.rolling_mean(timeseries, window=12)\n",
    "    rolstd = pd.rolling_std(timeseries, window=12)\n",
    "\n",
    "    #Plot rolling statistics:\n",
    "    orig = plt.plot(timeseries, color='blue',label='Original')\n",
    "    mean = plt.plot(rolmean, color='red', label='Rolling Mean')\n",
    "    std = plt.plot(rolstd, color='black', label = 'Rolling Std')\n",
    "    plt.legend(loc='best')\n",
    "    plt.title('Rolling Mean & Standard Deviation')\n",
    "    plt.show(block=False)\n",
    "    \n",
    "    #Perform Dickey-Fuller test:\n",
    "    print ('Results of Dickey-Fuller Test:')\n",
    "    dftest = adfuller(timeseries, autolag='AIC')\n",
    "    dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])\n",
    "    for key,value in dftest[4].items():\n",
    "        dfoutput['Critical Value (%s)'%key] = value\n",
    "    print (dfoutput)\n",
    "    with open(\"Results\\ADF.txt\", \"w\") as text_file:\n",
    "        print(dfoutput, file=text_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: FutureWarning: pd.rolling_mean is deprecated for Series and will be removed in a future version, replace with \n",
      "\tSeries.rolling(window=12,center=False).mean()\n",
      "  \"\"\"\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:6: FutureWarning: pd.rolling_std is deprecated for Series and will be removed in a future version, replace with \n",
      "\tSeries.rolling(window=12,center=False).std()\n",
      "  \n"
     ]
    },
    {
     "data": {
      "image/png": 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02bJlizz++GyB++TSS68X6Cx+fnWkSZMm0qFDBxkwYIC899578tFH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\nEcn4f7/WQGzj6iCHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4de5438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results of Dickey-Fuller Test:\n",
      "Test Statistic                  -5.145614\n",
      "p-value                          0.000011\n",
      "#Lags Used                      19.000000\n",
      "Number of Observations Used    487.000000\n",
      "Critical Value (1%)             -3.443849\n",
      "Critical Value (5%)             -2.867493\n",
      "Critical Value (10%)            -2.569941\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "test_stationarity(df['Return'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V3njDnonrrrMecj733mvn8vOfWz6vEVkIQ00QkRNhYSiMGjWqcztZssQKg2rQ3t6xtjRy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xca25a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df['Return'],'r')\n",
    "plt.savefig('Results/plot-0709.png',dpi=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf,plot_pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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f/sDPz+iqGt6MKEmSOpHBeZ6odAWLh/aweGgP16xdMaNtNd+MCGNvRpyptjt5ub1Ofm6S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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc659e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax1 = fig.add_subplot(211)\n",
    "fig = sm.graphics.tsa.plot_acf(df['Return'].dropna(),lags=22,ax=ax1)\n",
    "ax2 = fig.add_subplot(212)\n",
    "fig = sm.graphics.tsa.plot_pacf(df['Return'].dropna(),lags=22,ax=ax2)\n",
    "fig.savefig('Results/acf22-0709.png',dpi=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ARMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p_max=7\n",
    "q_max=7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p_list = []\n",
    "q_list = []\n",
    "AIC_list = []\n",
    "BIC_list = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "minAIC = 0\n",
    "minBIC = 0\n",
    "pminAIC = 0\n",
    "pminBIC = 0\n",
    "qminAIC = 0\n",
    "qminBIC = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:473: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:496: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  \"Check mle_retvals\", ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "#warnings.filterwarnings('ignore')\n",
    "for p in range (0,p_max):\n",
    "    for q in range (0,q_max):\n",
    "        try:\n",
    "            model = statsmodels.tsa.arima_model.ARIMA(df['Return'],order=(p,2,q))\n",
    "            results = model.fit(maxiter=1000)\n",
    "            p_list.append(p)\n",
    "            q_list.append(q)\n",
    "            AIC_list.append(results.aic)\n",
    "            BIC_list.append(results.bic)\n",
    "            if minAIC>results.aic:\n",
    "                minAIC = results.aic\n",
    "                pminAIC = p\n",
    "                qminAIC = q\n",
    "            if minBIC>results.bic:\n",
    "                minBIC = results.bic\n",
    "                pminBIC = p\n",
    "                qminBIC = q\n",
    "        except:\n",
    "            continue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "results = {'p':p_list,'q':q_list,'AIC':AIC_list,'BIC':BIC_list}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models = pd.DataFrame(data=results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models['AIC'] = models['AIC']/len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models['BIC'] = models['BIC']/len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AIC</th>\n",
       "      <th>BIC</th>\n",
       "      <th>p</th>\n",
       "      <th>q</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>-5.493600</td>\n",
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       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-5.571855</td>\n",
       "      <td>-5.488530</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
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       "      <th>10</th>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-5.191386</td>\n",
       "      <td>-5.141391</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-5.586001</td>\n",
       "      <td>-5.486011</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-5.315067</td>\n",
       "      <td>-5.256740</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-5.586520</td>\n",
       "      <td>-5.519861</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-5.576317</td>\n",
       "      <td>-5.501325</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-5.555147</td>\n",
       "      <td>-5.471822</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-5.372278</td>\n",
       "      <td>-5.305618</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-5.583476</td>\n",
       "      <td>-5.508484</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-5.587014</td>\n",
       "      <td>-5.503690</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-5.571065</td>\n",
       "      <td>-5.479408</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>-5.575103</td>\n",
       "      <td>-5.475114</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         AIC       BIC  p  q\n",
       "0  -4.442728 -4.426063  0  0\n",
       "1  -5.359008 -5.334011  0  1\n",
       "2  -4.774104 -4.749107  1  0\n",
       "3  -5.586698 -5.528370  1  4\n",
       "4  -5.570523 -5.503864  1  5\n",
       "5  -5.575353 -5.500361  1  6\n",
       "6  -4.985054 -4.951724  2  0\n",
       "7  -5.568592 -5.493600  2  5\n",
       "8  -5.571855 -5.488530  2  6\n",
       "9  -5.110253 -5.068590  3  0\n",
       "10 -5.566438 -5.474781  3  6\n",
       "11 -5.191386 -5.141391  4  0\n",
       "12 -5.586001 -5.486011  4  6\n",
       "13 -5.315067 -5.256740  5  0\n",
       "14 -5.586520 -5.519861  5  1\n",
       "15 -5.576317 -5.501325  5  2\n",
       "16 -5.555147 -5.471822  5  3\n",
       "17 -5.372278 -5.305618  6  0\n",
       "18 -5.583476 -5.508484  6  1\n",
       "19 -5.587014 -5.503690  6  2\n",
       "20 -5.571065 -5.479408  6  3\n",
       "21 -5.575103 -5.475114  6  4"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models.to_excel('Results/models0709.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'According to AIC, the minimum AIC value is -2897.275440862778 at p=4 and q=4.\\nAccording to BIC, the minimum BIC value is -2860.46530184 at p=1 and q=2.\\n'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Str_conclusion = 'According to AIC, the minimum AIC value is '+str(minAIC)+' at p='+str(pminAIC)+' and q='+str(qminAIC)+'.\\n'+'According to BIC, the minimum BIC value is '+str(minBIC)+' at p='+str(pminBIC)+' and q='+str(qminBIC)+'.\\n'\n",
    "with open(\"Results/ARMA_chosen_model(07-09).txt\", \"w\") as text_file:\n",
    "        print(Str_conclusion, file=text_file)\n",
    "Str_conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "On entry to DLASCL parameter number 4 had an illegal value",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-56-4c2e9bc7bafb>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mmodel\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtsa\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mARMA\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Return'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0morder\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmaxiter\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mStr_conclusion\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mres\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msummary\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Results/ARMA_summary.txt\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"w\"\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mtext_file\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\arima_model.py\u001b[0m in \u001b[0;36mfit\u001b[1;34m(self, start_params, trend, method, transparams, solver, maxiter, full_output, disp, callback, start_ar_lags, **kwargs)\u001b[0m\n\u001b[0;32m    967\u001b[0m                                        \u001b[0mmaxiter\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmaxiter\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    968\u001b[0m                                        \u001b[0mfull_output\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdisp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdisp\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 969\u001b[1;33m                                        callback=callback, **kwargs)\n\u001b[0m\u001b[0;32m    970\u001b[0m         \u001b[0mparams\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmlefit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    971\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py\u001b[0m in \u001b[0;36mfit\u001b[1;34m(self, start_params, method, maxiter, full_output, disp, fargs, callback, retall, skip_hessian, **kwargs)\u001b[0m\n\u001b[0;32m    449\u001b[0m                                                        \u001b[0mcallback\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mcallback\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    450\u001b[0m                                                        \u001b[0mretall\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mretall\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 451\u001b[1;33m                                                        full_output=full_output)\n\u001b[0m\u001b[0;32m    452\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    453\u001b[0m         \u001b[1;31m#NOTE: this is for fit_regularized and should be generalized\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\base\\optimizer.py\u001b[0m in \u001b[0;36m_fit\u001b[1;34m(self, objective, gradient, start_params, fargs, kwargs, hessian, method, maxiter, full_output, disp, callback, retall)\u001b[0m\n\u001b[0;32m    182\u001b[0m                             \u001b[0mdisp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdisp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmaxiter\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmaxiter\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mcallback\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    183\u001b[0m                             \u001b[0mretall\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mretall\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 184\u001b[1;33m                             hess=hessian)\n\u001b[0m\u001b[0;32m    185\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    186\u001b[0m         optim_settings = {'optimizer': method, 'start_params': start_params,\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\base\\optimizer.py\u001b[0m in \u001b[0;36m_fit_lbfgs\u001b[1;34m(f, score, start_params, fargs, kwargs, disp, maxiter, callback, retall, full_output, hess)\u001b[0m\n\u001b[0;32m    376\u001b[0m                                          \u001b[0mcallback\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mcallback\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfargs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    377\u001b[0m                                          \u001b[0mbounds\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mbounds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdisp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdisp\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 378\u001b[1;33m                                          **extra_kwargs)\n\u001b[0m\u001b[0;32m    379\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    380\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\lbfgsb.py\u001b[0m in \u001b[0;36mfmin_l_bfgs_b\u001b[1;34m(func, x0, fprime, args, approx_grad, bounds, m, factr, pgtol, epsilon, iprint, maxfun, maxiter, disp, callback, maxls)\u001b[0m\n\u001b[0;32m    191\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    192\u001b[0m     res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds,\n\u001b[1;32m--> 193\u001b[1;33m                            **opts)\n\u001b[0m\u001b[0;32m    194\u001b[0m     d = {'grad': res['jac'],\n\u001b[0;32m    195\u001b[0m          \u001b[1;34m'task'\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mres\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'message'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\lbfgsb.py\u001b[0m in \u001b[0;36m_minimize_lbfgsb\u001b[1;34m(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, maxls, **unknown_options)\u001b[0m\n\u001b[0;32m    326\u001b[0m             \u001b[1;31m# until the completion of the current minimization iteration.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    327\u001b[0m             \u001b[1;31m# Overwrite f and g:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 328\u001b[1;33m             \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc_and_grad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    329\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0mtask_str\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstartswith\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34mb'NEW_X'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    330\u001b[0m             \u001b[1;31m# new iteration\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\lbfgsb.py\u001b[0m in \u001b[0;36mfunc_and_grad\u001b[1;34m(x)\u001b[0m\n\u001b[0;32m    271\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mjac\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    272\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0mfunc_and_grad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 273\u001b[1;33m             \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    274\u001b[0m             \u001b[0mg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_approx_fprime_helper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mf0\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    275\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[1;34m(*wrapper_args)\u001b[0m\n\u001b[0;32m    290\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    291\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 292\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    293\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    294\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(params, *args)\u001b[0m\n\u001b[0;32m    427\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    428\u001b[0m         \u001b[0mnobs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mendog\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 429\u001b[1;33m         \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloglike\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mnobs\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    430\u001b[0m         \u001b[0mscore\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscore\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mnobs\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    431\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\arima_model.py\u001b[0m in \u001b[0;36mloglike\u001b[1;34m(self, params, set_sigma2)\u001b[0m\n\u001b[0;32m    788\u001b[0m         \u001b[0mmethod\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    789\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mmethod\u001b[0m \u001b[1;32min\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'mle'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'css-mle'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 790\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloglike_kalman\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mset_sigma2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    791\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0mmethod\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'css'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    792\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloglike_css\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mset_sigma2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\arima_model.py\u001b[0m in \u001b[0;36mloglike_kalman\u001b[1;34m(self, params, set_sigma2)\u001b[0m\n\u001b[0;32m    798\u001b[0m         \u001b[0mCompute\u001b[0m \u001b[0mexact\u001b[0m \u001b[0mloglikelihood\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mARMA\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mp\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mq\u001b[0m\u001b[1;33m)\u001b[0m \u001b[0mmodel\u001b[0m \u001b[0mby\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mKalman\u001b[0m \u001b[0mFilter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    799\u001b[0m         \"\"\"\n\u001b[1;32m--> 800\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mKalmanFilter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloglike\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mset_sigma2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    801\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    802\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mloglike_css\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mset_sigma2\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\kalmanf\\kalmanfilter.py\u001b[0m in \u001b[0;36mloglike\u001b[1;34m(cls, params, arma_model, set_sigma2)\u001b[0m\n\u001b[0;32m    647\u001b[0m             loglike, sigma2 =  kalman_loglike.kalman_loglike_double(y, k,\n\u001b[0;32m    648\u001b[0m                                     \u001b[0mk_ar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mk_ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mk_lags\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnobs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mZ_mat\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 649\u001b[1;33m                                     R_mat, T_mat)\n\u001b[0m\u001b[0;32m    650\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0missubdtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparamsdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcomplex\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    651\u001b[0m             loglike, sigma2 =  kalman_loglike.kalman_loglike_complex(y, k,\n",
      "\u001b[1;32mstatsmodels\\tsa\\kalmanf\\kalman_loglike.pyx\u001b[0m in \u001b[0;36mstatsmodels.tsa.kalmanf.kalman_loglike.kalman_loglike_double (statsmodels/tsa/kalmanf/kalman_loglike.c:6510)\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mstatsmodels\\tsa\\kalmanf\\kalman_loglike.pyx\u001b[0m in \u001b[0;36mstatsmodels.tsa.kalmanf.kalman_loglike.kalman_filter_double (statsmodels/tsa/kalmanf/kalman_loglike.c:3560)\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36mpinv\u001b[1;34m(a, rcond)\u001b[0m\n\u001b[0;32m   1660\u001b[0m     \u001b[0m_assertNoEmpty2d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1661\u001b[0m     \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mconjugate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1662\u001b[1;33m     \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msvd\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1663\u001b[0m     \u001b[0mm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1664\u001b[0m     \u001b[0mn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mvt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36msvd\u001b[1;34m(a, full_matrices, compute_uv)\u001b[0m\n\u001b[0;32m   1402\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1403\u001b[0m         \u001b[0msignature\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m'D->DdD'\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32melse\u001b[0m \u001b[1;34m'd->ddd'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1404\u001b[1;33m         \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgufunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1405\u001b[0m         \u001b[0mu\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1406\u001b[0m         \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_realType\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: On entry to DLASCL parameter number 4 had an illegal value"
     ]
    }
   ],
   "source": [
    "model = sm.tsa.ARMA(df['Return'],order=(5,5))\n",
    "res = model.fit(maxiter=1000)\n",
    "\n",
    "Str_conclusion = str(res.summary())\n",
    "with open(\"Results/ARMA_summary.txt\", \"w\") as text_file:\n",
    "        print(Str_conclusion, file=text_file)\n",
    "Str_conclusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'                              ARMA Model Results                              \\n==============================================================================\\nDep. Variable:                 Return   No. Observations:                  760\\nModel:                     ARMA(1, 2)   Log Likelihood                2207.273\\nMethod:                       css-mle   S.D. of innovations              0.013\\nDate:                Thu, 02 Nov 2017   AIC                          -4404.546\\nTime:                        20:32:17   BIC                          -4381.379\\nSample:                    01-02-2007   HQIC                         -4395.624\\n                         - 12-31-2009                                         \\n================================================================================\\n                   coef    std err          z      P>|z|      [0.025      0.975]\\n--------------------------------------------------------------------------------\\nconst           -0.0040      0.002     -2.381      0.017      -0.007      -0.001\\nar.L1.Return     0.8755      0.038     23.018      0.000       0.801       0.950\\nma.L1.Return    -0.3578      0.055     -6.460      0.000      -0.466      -0.249\\nma.L2.Return    -0.2070      0.044     -4.722      0.000      -0.293      -0.121\\n                                    Roots                                    \\n=============================================================================\\n                 Real           Imaginary           Modulus         Frequency\\n-----------------------------------------------------------------------------\\nAR.1            1.1422           +0.0000j            1.1422            0.0000\\nMA.1            1.4974           +0.0000j            1.4974            0.0000\\nMA.2           -3.2255           +0.0000j            3.2255            0.5000\\n-----------------------------------------------------------------------------'"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.tsa.ARMA(df['Return'],order=(pminBIC,qminBIC))\n",
    "res = model.fit(maxiter=1000)\n",
    "\n",
    "Str_conclusion = str(res.summary())\n",
    "with open(\"Results/ARMA_summary.txt\", \"w\") as text_file:\n",
    "        print(Str_conclusion, file=text_file)\n",
    "Str_conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model Diagnostics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.diagnostic import acorr_ljungbox as LB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = [pd.Series(range(1,11)),pd.Series(LB(res.resid,lags=10)[0])]\n",
    "Lbt = pd.concat(result,axis=1)\n",
    "Lbt.columns=['lags','Test Result']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Lbt.to_excel('Results/Ljung-Box Test.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.stattools import jarque_bera as JB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "result = JB(res.resid)\n",
    "JBResult = 'Jarque-Bera: '+ str(result[0])+'\\n p-value:' + str(result[1])+'\\n Skewness:' + str(result[2])+'\\n Kurtosis:' + str(result[3])\n",
    "with open(\"Results/Jarque-Bera.txt\", \"w\") as text_file:\n",
    "        print(JBResult, file=text_file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use p=1, q=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "first_day = 0\n",
    "forecast_day = len(df)\n",
    "forecast = []\n",
    "df = df.append(df_forecast)\n",
    "last_day = len(df_forecast)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0,last_day):\n",
    "    in_sample = df.iloc[first_day:forecast_day-1]\n",
    "    model = sm.tsa.ARMA(in_sample['Return'],order=(1,2))\n",
    "    res = model.fit(maxiter=1000)\n",
    "    fore = res.forecast(1)[0][0]\n",
    "    forecast.append(fore)\n",
    "    first_day = first_day+1\n",
    "    forecast_day = forecast_day+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "forecast_data = pd.Series(data=forecast,index=df_forecast.index)\n",
    "df_forecast = pd.concat([df_forecast,forecast_data],axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df_forecast.columns=['Rate','Return','Forecast log']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_forecast['Forecast ARMA'] = np.exp(df_forecast['Forecast log'])*df_forecast['Rate'].shift(1)\n",
    "df_forecast['Forecast ARMA'].iloc[0] = np.exp(df_forecast['Forecast log'].iloc[0])*df['Rate'].iloc[-1]\n",
    "MAE_ARMA = np.average(np.abs(df_forecast['Rate']-df_forecast['Forecast ARMA']))\n",
    "Sum_Square = (df_forecast['Rate']-df_forecast['Forecast ARMA'])**2\n",
    "RMSE_ARMA = np.sqrt(np.average(Sum_Square))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_forecast['Naive'] = df_forecast['Rate'].shift(1)\n",
    "df_forecast['Naive'].iloc[0] = df['Rate'].iloc[-1]\n",
    "MAE_naive = np.average(np.abs(df_forecast['Rate']-df_forecast['Naive']))\n",
    "Sum_Square_naive = (df_forecast['Rate']-df_forecast['Naive'])**2\n",
    "RMSE_naive = np.sqrt(np.average(Sum_Square_naive))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xc997198>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ArgrGR54xBntliv0dY9CccSvx/aad7NpbTX/fSug8ioGdYnnl6hHUWBZ/KxoOOQuwHuoA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc9be748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_forecast[['Rate','Forecast ARMA']].plot(figsize=(12,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ARMA-GARCH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xc79f2e8>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gx7jjB68ivE2JcTckUBUF8O6v4R8zoGxPq0u2FlQyxNv42TEd9xi3EDcAvr8I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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xca06278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_armagarch = pd.read_excel('Results\\Forecast.xls',index_col='Date')\n",
    "df_armagarch['Forecast_ARMAGARCH'] = np.exp(df_armagarch['Forecast'])*df_armagarch['Rate'].shift(1)\n",
    "df_armagarch['Forecast_ARMAGARCH'].iloc[0] = np.exp(df_armagarch['Forecast'].iloc[0])*df['Rate'].iloc[-1]\n",
    "df_forecast = df_forecast.merge(pd.DataFrame(df_armagarch),how='left')\n",
    "df_forecast.drop('Forecast',axis=1,inplace=True)\n",
    "df_forecast.drop('Residuals',axis=1,inplace=True)\n",
    "df_forecast.to_excel('Results/Prediction 2009 (model 2007-2008).xls')\n",
    "MAE_ag = np.average(np.abs(df_forecast['Rate']-df_forecast['Forecast_ARMAGARCH']))\n",
    "Sum_Square_ag = (df_forecast['Rate']-df_forecast['Forecast_ARMAGARCH'])**2\n",
    "RMSE_ag = np.sqrt(np.average(Sum_Square_ag))\n",
    "df_forecast[['Rate','Forecast_ARMAGARCH']].plot(figsize=(12,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forecast Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "title = ['Naive','ARMA','ARMA-Garch']\n",
    "obs = [str(len(df_forecast)),str(len(df_forecast)),str(len(df_forecast))]\n",
    "no1 = [RMSE_naive,RMSE_ARMA,RMSE_ag]\n",
    "no2 = [MAE_naive,MAE_ARMA,MAE_ag]\n",
    "result = pd.DataFrame(np.transpose([obs,no1,no2]),index=title,columns=['Number of Observations','RMSE','MAE'])\n",
    "result.to_excel('Results/Forecast_Result.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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