ARMA-2010-2017 12M.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.read_excel('12monthsnew data.xls',sheetname='data to use',index_col='Date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.columns = ['Rate','Return']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_forecast = df.loc['20160101':'20171231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.loc['20100101':'20151231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "461"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_forecast)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.to_excel('Results/in-sample.xls')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stationary Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "max_lag = math.floor(len(df)**1/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def adf_check(time_series):\n",
    "    \"\"\"\n",
    "    Pass in a time series, returns ADF report\n",
    "    \"\"\"\n",
    "    result = adfuller(time_series,maxlag=max_lag)\n",
    "    string = \"\"\n",
    "    string += 'Augmented Dickey-Fuller Test:\\n'\n",
    "    labels = ['ADF Test Statistic','p-value','#Lags Used','Number of Observations Used']\n",
    "\n",
    "    for value,label in zip(result,labels):\n",
    "        string += label+' : '+str(value)+'\\n'\n",
    "    \n",
    "    if result[1] <= 0.05:\n",
    "        string += \"strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\"\n",
    "    else:\n",
    "        string += \"weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \"\n",
    "        \n",
    "    print(string)\n",
    "    with open(\"ADF-0005.txt\", \"w\") as text_file:\n",
    "        print(string, file=text_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Augmented Dickey-Fuller Test:\n",
      "ADF Test Statistic : -3.55184887641\n",
      "p-value : 0.00675117743494\n",
      "#Lags Used : 32\n",
      "Number of Observations Used : 1482\n",
      "strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\n"
     ]
    }
   ],
   "source": [
    "adf_check(df['Return'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
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UzjorPCPr2hW4+uqSqwgAePJJ7znWiaGfO+6IFyfACEPajGTrrcv32RK931WK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc5eb588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df['Return'],'r')\n",
    "plt.savefig('Results/plot.png',dpi=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf,plot_pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZleRgU8d3NNOn265bk7ylebwoyTuT7EyyL8mHknxDM2910/v+xiRfSfJwkv/U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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc579e10>"
      ]
     },
     "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.png',dpi=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Model choosing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p_max=7\n",
    "q_max=7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p_list = []\n",
    "q_list = []\n",
    "AIC_list = []\n",
    "BIC_list = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:584: RuntimeWarning: overflow encountered in exp\n",
      "  newparams = ((1-np.exp(-params))/\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:585: RuntimeWarning: overflow encountered in exp\n",
      "  (1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:585: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:586: RuntimeWarning: overflow encountered in exp\n",
      "  tmp = ((1-np.exp(-params))/\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:587: RuntimeWarning: overflow encountered in exp\n",
      "  (1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:587: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:628: RuntimeWarning: overflow encountered in exp\n",
      "  newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:628: RuntimeWarning: invalid value encountered in true_divide\n",
      "  newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:629: RuntimeWarning: overflow encountered in exp\n",
      "  tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:629: RuntimeWarning: invalid value encountered in true_divide\n",
      "  tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\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 = sm.tsa.ARMA(df['Return'],order=(p,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": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "results = {'p':p_list,'q':q_list,'AIC':AIC_list,'BIC':BIC_list}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models = pd.DataFrame(data=results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'According to AIC, the minimum AIC value is -14064.038277292024 at p=3 and q=3.\\nAccording to BIC, the minimum BIC value is -14033.0413344 at p=1 and q=1.\\n'"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models['AIC'] = models['AIC']/len(df)\n",
    "models['BIC'] = models['BIC']/len(df)\n",
    "models.to_excel('Results/models1015.xls')\n",
    "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(10-15).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": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'                              ARMA Model Results                              \\n==============================================================================\\nDep. Variable:                 Return   No. Observations:                 1515\\nModel:                     ARMA(1, 1)   Log Likelihood                5374.732\\nMethod:                       css-mle   S.D. of innovations              0.007\\nDate:                Wed, 27 Dec 2017   AIC                         -10741.464\\nTime:                        18:14:56   BIC                         -10720.172\\nSample:                    01-04-2010   HQIC                        -10733.536\\n                         - 12-31-2015                                         \\n================================================================================\\n                   coef    std err          z      P>|z|      [0.025      0.975]\\n--------------------------------------------------------------------------------\\nconst            0.0001      0.001      0.175      0.861      -0.001       0.002\\nar.L1.Return     0.9795      0.008    120.402      0.000       0.964       0.995\\nma.L1.Return    -0.9104      0.014    -63.700      0.000      -0.938      -0.882\\n                                    Roots                                    \\n=============================================================================\\n                 Real           Imaginary           Modulus         Frequency\\n-----------------------------------------------------------------------------\\nAR.1            1.0210           +0.0000j            1.0210            0.0000\\nMA.1            1.0984           +0.0000j            1.0984            0.0000\\n-----------------------------------------------------------------------------'"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.tsa.ARMA(df['Return'],order=(1,1))\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 Diagnostic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.diagnostic import acorr_ljungbox as LB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Lbt.to_excel('Results/Ljung-Box Test.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.stattools import jarque_bera as JB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "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=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "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",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:628: RuntimeWarning: overflow encountered in exp\n",
      "  newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:628: RuntimeWarning: invalid value encountered in true_divide\n",
      "  newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:629: RuntimeWarning: overflow encountered in exp\n",
      "  tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:629: RuntimeWarning: invalid value encountered in true_divide\n",
      "  tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\kalmanf\\kalmanfilter.py:649: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  R_mat, T_mat)\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:584: RuntimeWarning: overflow encountered in exp\n",
      "  newparams = ((1-np.exp(-params))/\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:585: RuntimeWarning: overflow encountered in exp\n",
      "  (1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:585: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:586: RuntimeWarning: overflow encountered in exp\n",
      "  tmp = ((1-np.exp(-params))/\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:587: RuntimeWarning: overflow encountered in exp\n",
      "  (1+np.exp(-params))).copy()\n",
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:587: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (1+np.exp(-params))).copy()\n"
     ]
    }
   ],
   "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=(3,3))\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": 75,
   "metadata": {
    "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": 76,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df_forecast.columns=['Rate','Return','Forecast log']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "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": 78,
   "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": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xc8a9da0>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0yjFRAR60DQvgN2MPOLRaCnvVNE1j7def0leXQNklL4JnsLNDumBSMRZCCNFs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\nFVy49vsc7toAQ76012tcLsP4/LTdP+xohTBAUVYSV50wlu9/bgwvri7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teC57ltq2KD9+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\n+ToUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc948278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_forecast[['Rate','Forecast ARMA']].plot(figsize=(12,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": true
   },
   "source": [
    "<h1>ARMA-GARCH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xcb17c88>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vhBBCNJOM4ipClUI0qgX8Ws86qyHeRo6pEfU1xtml9g1K/NQSe7b4N0u1Xa4I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\nKO1adgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcb17198>"
      ]
     },
     "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": [
    "<h1>Forecast Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "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": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}