ARIMA-2010-2017 12M.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.read_excel('12monthsnew data.xls',sheetname='data to use',index_col='Date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.columns = ['Rate','Return']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_forecast = df.loc['20160101':'20171231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.loc['20100101':'20151231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "461"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_forecast)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.to_excel('Results/in-sample.xls')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use p=0, q=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\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\\base\\model.py:496: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  \"Check mle_retvals\", ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "for i in range(0,last_day):\n",
    "    in_sample = df.iloc[first_day:forecast_day-1]\n",
    "    model = statsmodels.tsa.arima_model.ARIMA(in_sample['Return'],order=(0,1,1))\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": 23,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df_forecast.columns=['Rate','Return','Forecast log']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "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": 25,
   "metadata": {
    "collapsed": true
   },
   "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": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0081646347443477367"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MAE_ARMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.033460632630809152"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RMSE_ARMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xc70ed68>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OcK167dSzVIzPpX9bP/67dRA3tFiN4eu7IfI6COwMrfqDt7Siib+2hOxSHlq+j8CMjbzv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\nMYA7xsYYY4wxxgDuGBtjjDHGGAPA/wGINjWSxpYEogAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc70e320>"
      ]
     },
     "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
}