ARIMA-2010-2017 3M.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels as sm\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.read_excel('newdata3month.xls',sheetname='data to use',index_col='Date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_forecast = df.loc['20160101':'20171231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = df.loc['20100101':'20151231',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.to_excel('Results/in-sample.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "460"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_forecast)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stationary Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "max_lag = math.floor(len(df)**1/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "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": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Augmented Dickey-Fuller Test:\n",
      "ADF Test Statistic : -4.31462882973\n",
      "p-value : 0.000419002787827\n",
      "#Lags Used : 35\n",
      "Number of Observations Used : 1479\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": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MTSsw2LLGI4/MPV/UwCBS/MDgvQJraAD+9rfifh8APP+8OdAB90+bpBuAIO/VkjVlSvhN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x133c7be0>"
      ]
     },
     "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": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf,plot_pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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is8Aq4HRgL/BR4K+BzwFnAzuBn81ML7zqYxO8T1ZRW0aRwKPA+xrWkaoPRcRb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\nwRgAACrBGAAAKsEYAACq+gRO0c8CqV2F0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1c88d0>"
      ]
     },
     "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": 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": {},
   "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\\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.arima_model.ARIMA(df['Return'],order=(p,1,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": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "results = {'p':p_list,'q':q_list,'AIC':AIC_list,'BIC':BIC_list}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models = pd.DataFrame(data=results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'According to AIC, the minimum AIC value is -10562.089349565405 at p=6 and q=4.\\nAccording to BIC, the minimum BIC value is -10542.5231657 at p=0 and q=1.\\n'"
      ]
     },
     "execution_count": 15,
     "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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'                             ARIMA Model Results                              \\n==============================================================================\\nDep. Variable:               D.Return   No. Observations:                 1514\\nModel:                 ARIMA(0, 1, 1)   Log Likelihood                5282.245\\nMethod:                       css-mle   S.D. of innovations              0.007\\nDate:                Sun, 12 Nov 2017   AIC                         -10558.491\\nTime:                        11:38:44   BIC                         -10542.523\\nSample:                    01-05-2010   HQIC                        -10552.545\\n                         - 12-31-2015                                         \\n==================================================================================\\n                     coef    std err          z      P>|z|      [0.025      0.975]\\n----------------------------------------------------------------------------------\\nconst            7.65e-06   2.91e-05      0.263      0.792   -4.93e-05    6.46e-05\\nma.L1.D.Return    -0.8474      0.013    -63.670      0.000      -0.874      -0.821\\n                                    Roots                                    \\n=============================================================================\\n                 Real           Imaginary           Modulus         Frequency\\n-----------------------------------------------------------------------------\\nMA.1            1.1800           +0.0000j            1.1800            0.0000\\n-----------------------------------------------------------------------------'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = statsmodels.tsa.arima_model.ARIMA(df['Return'],order=(0,1,1))\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": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.diagnostic import acorr_ljungbox as LB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "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": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Lbt.to_excel('Results/Ljung-Box Test.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.stattools import jarque_bera as JB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "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=0, q=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": 17,
   "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"
     ]
    }
   ],
   "source": [
    "import statsmodels.api\n",
    "for i in range(0,last_day):\n",
    "    in_sample = df.iloc[first_day:forecast_day-1].dropna()\n",
    "    model = statsmodels.tsa.arima_model.ARIMA(in_sample['Return'],order=(0,0,1))\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": 18,
   "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": 19,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df_forecast.columns=['Rate','Return','Forecast log']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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": 21,
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.036303331237068505"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RMSE_ARMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0049921898379433876"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MAE_ARMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xc708a58>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oLikhL6wVoTYbd/5ByD8IgWGUdLqE4rwsghOXQMN20KQzhMdATgokzAa/D5rFQ/PuAHyz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xca81a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_forecast[['Rate','Forecast ARMA']].plot(figsize=(12,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>ARMA-GARCH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: 'Results\\\\Forecast.xls'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-23-0725e58b3af1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mdf_armagarch\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mread_excel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Results\\Forecast.xls'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mindex_col\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'Date'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mdf_armagarch\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Forecast_ARMAGARCH'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf_armagarch\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Forecast'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mdf_armagarch\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Rate'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshift\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[0;32m      3\u001b[0m \u001b[0mdf_armagarch\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Forecast_ARMAGARCH'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf_armagarch\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Forecast'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Rate'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[1;33m[\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[0;32m      4\u001b[0m \u001b[0mdf_forecast\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf_forecast\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmerge\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf_armagarch\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mhow\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'left'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mdf_forecast\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdrop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Forecast'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0minplace\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\io\\excel.py\u001b[0m in \u001b[0;36mread_excel\u001b[1;34m(io, sheetname, header, skiprows, skip_footer, index_col, names, parse_cols, parse_dates, date_parser, na_values, thousands, convert_float, has_index_names, converters, dtype, true_values, false_values, engine, squeeze, **kwds)\u001b[0m\n\u001b[0;32m    198\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    199\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mio\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mExcelFile\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 200\u001b[1;33m         \u001b[0mio\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mExcelFile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mio\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mengine\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mengine\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    201\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    202\u001b[0m     return io._parse_excel(\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\io\\excel.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, io, **kwds)\u001b[0m\n\u001b[0;32m    255\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbook\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mxlrd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mopen_workbook\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfile_contents\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    256\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mio\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcompat\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstring_types\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 257\u001b[1;33m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbook\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mxlrd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mopen_workbook\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mio\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    258\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    259\u001b[0m             raise ValueError('Must explicitly set engine if not passing in'\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\xlrd\\__init__.py\u001b[0m in \u001b[0;36mopen_workbook\u001b[1;34m(filename, logfile, verbosity, use_mmap, file_contents, encoding_override, formatting_info, on_demand, ragged_rows)\u001b[0m\n\u001b[0;32m    393\u001b[0m         \u001b[0mpeek\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfile_contents\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mpeeksz\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    394\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 395\u001b[1;33m         \u001b[1;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfilename\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"rb\"\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    396\u001b[0m             \u001b[0mpeek\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mread\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpeeksz\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    397\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mpeek\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34mb\"PK\\x03\\x04\"\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;31m# a ZIP file\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: 'Results\\\\Forecast.xls'"
     ]
    }
   ],
   "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 Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Shape of passed values is (1, 3), indices imply (3, 2)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\internals.py\u001b[0m in \u001b[0;36mcreate_block_manager_from_blocks\u001b[1;34m(blocks, axes)\u001b[0m\n\u001b[0;32m   4293\u001b[0m                 blocks = [make_block(values=blocks[0],\n\u001b[1;32m-> 4294\u001b[1;33m                                      placement=slice(0, len(axes[0])))]\n\u001b[0m\u001b[0;32m   4295\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\internals.py\u001b[0m in \u001b[0;36mmake_block\u001b[1;34m(values, placement, klass, ndim, dtype, fastpath)\u001b[0m\n\u001b[0;32m   2718\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2719\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mklass\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mndim\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mndim\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfastpath\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfastpath\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mplacement\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mplacement\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2720\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\internals.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, values, ndim, fastpath, placement, **kwargs)\u001b[0m\n\u001b[0;32m   1843\u001b[0m         super(ObjectBlock, self).__init__(values, ndim=ndim, fastpath=fastpath,\n\u001b[1;32m-> 1844\u001b[1;33m                                           placement=placement, **kwargs)\n\u001b[0m\u001b[0;32m   1845\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\internals.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, values, placement, ndim, fastpath)\u001b[0m\n\u001b[0;32m    114\u001b[0m                              'implies %d' % (len(self.values),\n\u001b[1;32m--> 115\u001b[1;33m                                              len(self.mgr_locs)))\n\u001b[0m\u001b[0;32m    116\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: Wrong number of items passed 1, placement implies 3",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-24-49bb8bab2ae4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mno1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mRMSE_naive\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mRMSE_ARMA\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mno2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mMAE_naive\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mMAE_ARMA\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mobs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mno1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mno2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtitle\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Number of Observations'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'RMSE'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'MAE'\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      6\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mto_excel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Results/Forecast_Result.xls'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\frame.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, data, index, columns, dtype, copy)\u001b[0m\n\u001b[0;32m    304\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    305\u001b[0m                 mgr = self._init_ndarray(data, index, columns, dtype=dtype,\n\u001b[1;32m--> 306\u001b[1;33m                                          copy=copy)\n\u001b[0m\u001b[0;32m    307\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtypes\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mGeneratorType\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    308\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtypes\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mGeneratorType\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\\pandas\\core\\frame.py\u001b[0m in \u001b[0;36m_init_ndarray\u001b[1;34m(self, values, index, columns, dtype, copy)\u001b[0m\n\u001b[0;32m    481\u001b[0m             \u001b[0mvalues\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmaybe_infer_to_datetimelike\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    482\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 483\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mcreate_block_manager_from_blocks\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mindex\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    484\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    485\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\internals.py\u001b[0m in \u001b[0;36mcreate_block_manager_from_blocks\u001b[1;34m(blocks, axes)\u001b[0m\n\u001b[0;32m   4301\u001b[0m         \u001b[0mblocks\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'values'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mb\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mblocks\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4302\u001b[0m         \u001b[0mtot_items\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\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;32mfor\u001b[0m \u001b[0mb\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mblocks\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4303\u001b[1;33m         \u001b[0mconstruction_error\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtot_items\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mblocks\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\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[1;33m,\u001b[0m \u001b[0maxes\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4304\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4305\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\core\\internals.py\u001b[0m in \u001b[0;36mconstruction_error\u001b[1;34m(tot_items, block_shape, axes, e)\u001b[0m\n\u001b[0;32m   4278\u001b[0m         \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Empty data passed with indices specified.\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4279\u001b[0m     raise ValueError(\"Shape of passed values is {0}, indices imply {1}\".format(\n\u001b[1;32m-> 4280\u001b[1;33m         passed, implied))\n\u001b[0m\u001b[0;32m   4281\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4282\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: Shape of passed values is (1, 3), indices imply (3, 2)"
     ]
    }
   ],
   "source": [
    "title = ['Naive','ARMA']\n",
    "obs = [str(len(df_forecast)),str(len(df_forecast)),str(len(df_forecast))]\n",
    "no1 = [RMSE_naive,RMSE_ARMA]\n",
    "no2 = [MAE_naive,MAE_ARMA]\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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