TimeSeriesErgasia - ex1-y2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Series Assignment\n",
    "\n",
    "* Student: **Perakis Georgios**\n",
    "* Code: **DS3616014**\n",
    "* Contact: **gperakis[at]aueb.gr**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data you will have to analyze are in the eclass in the **excel data-assignment.xls**\n",
    "file. The **dependent variables** for which you will construct the models you are asked\n",
    "for, are the **returns** of four investment vechicles **(Y1, Y2, Y3, Y4)** for the period **1/1991 - 12/2005**.\n",
    "\n",
    "The **independent variables** you will use in the models refer to **monthly** values/returns for the variables:\n",
    "* x1 = RUS-Rf\n",
    "* x2 = RUS (-1) -Rf (-1) lagged Russel index\n",
    "* x3 = MXUS-Rf\n",
    "* x4 = MEM- Rf\n",
    "* x5 = SMB\n",
    "* x6 = HML\n",
    "* x7 = MOM\n",
    "* x8 = SBGC-Rf\n",
    "* x9 = SBWG-Rf\n",
    "* x10 = LHY-Rf\n",
    "* x11 = DEFSPR\n",
    "* x12 = FRSI-Rf\n",
    "* x13 = GSCI-Rf\n",
    "* x14 = VIX\n",
    "\n",
    "for the period **1/1991 - 12/2005**.\n",
    "\n",
    "Analyze dependent variables based on data for the period 1/1991 - 12/2004 **[You will not use the data for the period 1/2005 - 12/2005]**:\n",
    "\n",
    "1. Construct an appropriate **time series** model (AR, MA, ARMA).\n",
    "2. Develop an appropriate **regression** model\n",
    "  * In case of **autocorrelation** problem of **regression residuals**, correct the autocorrelation problem (using time series AR, MA, ARMA models).\n",
    "  * In case of **heteroscedasticity** problem of **regression residuals**, correct the\n",
    "    heteroskedasticity problem (using time-varying ARCH, GARCH models).\n",
    "3. Write the models you have found at questions (1) - (2). Assess the **goodness of fit** of these models based on the **AIC and BIC** information criteria.\n",
    "4. Based on the estimated models of questions (1) - (2), **construct forecasts** of the analyzed series for the period **1/2005 - 12/2005**, and **evaluate the forecasts** you have found by using two evaluation criteria:\n",
    "  * the mean square prediction error\n",
    "  * the Hit ratio (indicates the percentage of predictions that correctly evaluate the sign of the actual value of the dependent variable.)\n",
    "  \n",
    "Each student will have to analyze **two only dependent variables**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loads the library urca, which contains the command ur.df() \n",
    "# and applies Unit-Root Testing based on Dickey-Fuller test \n",
    "library(urca)\n",
    "library(tseries)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing data into R can be carried out in various ways. Below, the command read.table is used:\n",
    "data_all = read.table('/home/socital1/Desktop/george/AUEB/TimeSeries/Assignment-February-2018/Data-Assignment-Feb-2018.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>V1</th><th scope=col>V2</th><th scope=col>V3</th><th scope=col>V4</th><th scope=col>V5</th><th scope=col>V6</th><th scope=col>V7</th><th scope=col>V8</th><th scope=col>V9</th><th scope=col>V10</th><th scope=col>V11</th><th scope=col>V12</th><th scope=col>V13</th><th scope=col>V14</th><th scope=col>V15</th><th scope=col>V16</th><th scope=col>V17</th><th scope=col>V18</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 0.02058</td><td> 0.02058</td><td> 0.00468</td><td>0.01468 </td><td> 0.04568</td><td> 0.01745</td><td> 0.02313</td><td> 0.07273</td><td> 0.0389 </td><td>-0.0181 </td><td>-0.0946 </td><td> 0.00575</td><td> 0.01937</td><td> 0.01868</td><td> 0.0001 </td><td> 0.00004</td><td>-0.10389</td><td>-0.0547 </td></tr>\n",
       "\t<tr><td> 0.03503</td><td> 0.02583</td><td> 0.03903</td><td>0.03623 </td><td> 0.06346</td><td> 0.04568</td><td> 0.09344</td><td> 0.13201</td><td> 0.0397 </td><td>-0.0056 </td><td>-0.1147 </td><td> 0.00144</td><td>-0.00486</td><td> 0.10639</td><td>-0.0014 </td><td>-0.01039</td><td> 0.00866</td><td> 0.0032 </td></tr>\n",
       "\t<tr><td> 0.04458</td><td> 0.02168</td><td> 0.02878</td><td>0.06348 </td><td> 0.02225</td><td> 0.06346</td><td>-0.06591</td><td> 0.03187</td><td> 0.0395 </td><td>-0.0124 </td><td>-0.0407 </td><td> 0.00253</td><td>-0.04193</td><td> 0.02621</td><td>-0.0024 </td><td> 0.03228</td><td> 0.03201</td><td>-0.0435 </td></tr>\n",
       "\t<tr><td> 0.00865</td><td> 0.01325</td><td> 0.02585</td><td>0.04855 </td><td>-0.00581</td><td> 0.02225</td><td> 0.00371</td><td>-0.00174</td><td> 0.0037 </td><td> 0.0170 </td><td>-0.0224 </td><td> 0.00790</td><td> 0.01053</td><td> 0.01619</td><td>-0.0008 </td><td> 0.01107</td><td> 0.01764</td><td> 0.0136 </td></tr>\n",
       "\t<tr><td> 0.01507</td><td> 0.00227</td><td> 0.02377</td><td>0.00887 </td><td> 0.03258</td><td>-0.00581</td><td> 0.00577</td><td> 0.06795</td><td>-0.0037 </td><td>-0.0052 </td><td> 0.0282 </td><td>-0.00023</td><td>-0.00601</td><td>-0.00780</td><td>-0.0011 </td><td> 0.00235</td><td>-0.00524</td><td>-0.0231 </td></tr>\n",
       "\t<tr><td>-0.00064</td><td>-0.00924</td><td>-0.00234</td><td>0.01246 </td><td>-0.05360</td><td> 0.03258</td><td>-0.07982</td><td>-0.04322</td><td> 0.0006 </td><td> 0.0102 </td><td> 0.0010 </td><td>-0.00499</td><td>-0.01526</td><td> 0.01826</td><td>-0.0011 </td><td> 0.01085</td><td>-0.02869</td><td> 0.0362 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllllllllll}\n",
       " V1 & V2 & V3 & V4 & V5 & V6 & V7 & V8 & V9 & V10 & V11 & V12 & V13 & V14 & V15 & V16 & V17 & V18\\\\\n",
       "\\hline\n",
       "\t  0.02058 &  0.02058 &  0.00468 & 0.01468  &  0.04568 &  0.01745 &  0.02313 &  0.07273 &  0.0389  & -0.0181  & -0.0946  &  0.00575 &  0.01937 &  0.01868 &  0.0001  &  0.00004 & -0.10389 & -0.0547 \\\\\n",
       "\t  0.03503 &  0.02583 &  0.03903 & 0.03623  &  0.06346 &  0.04568 &  0.09344 &  0.13201 &  0.0397  & -0.0056  & -0.1147  &  0.00144 & -0.00486 &  0.10639 & -0.0014  & -0.01039 &  0.00866 &  0.0032 \\\\\n",
       "\t  0.04458 &  0.02168 &  0.02878 & 0.06348  &  0.02225 &  0.06346 & -0.06591 &  0.03187 &  0.0395  & -0.0124  & -0.0407  &  0.00253 & -0.04193 &  0.02621 & -0.0024  &  0.03228 &  0.03201 & -0.0435 \\\\\n",
       "\t  0.00865 &  0.01325 &  0.02585 & 0.04855  & -0.00581 &  0.02225 &  0.00371 & -0.00174 &  0.0037  &  0.0170  & -0.0224  &  0.00790 &  0.01053 &  0.01619 & -0.0008  &  0.01107 &  0.01764 &  0.0136 \\\\\n",
       "\t  0.01507 &  0.00227 &  0.02377 & 0.00887  &  0.03258 & -0.00581 &  0.00577 &  0.06795 & -0.0037  & -0.0052  &  0.0282  & -0.00023 & -0.00601 & -0.00780 & -0.0011  &  0.00235 & -0.00524 & -0.0231 \\\\\n",
       "\t -0.00064 & -0.00924 & -0.00234 & 0.01246  & -0.05360 &  0.03258 & -0.07982 & -0.04322 &  0.0006  &  0.0102  &  0.0010  & -0.00499 & -0.01526 &  0.01826 & -0.0011  &  0.01085 & -0.02869 &  0.0362 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | \n",
       "|---|---|---|---|---|---|\n",
       "|  0.02058 |  0.02058 |  0.00468 | 0.01468  |  0.04568 |  0.01745 |  0.02313 |  0.07273 |  0.0389  | -0.0181  | -0.0946  |  0.00575 |  0.01937 |  0.01868 |  0.0001  |  0.00004 | -0.10389 | -0.0547  | \n",
       "|  0.03503 |  0.02583 |  0.03903 | 0.03623  |  0.06346 |  0.04568 |  0.09344 |  0.13201 |  0.0397  | -0.0056  | -0.1147  |  0.00144 | -0.00486 |  0.10639 | -0.0014  | -0.01039 |  0.00866 |  0.0032  | \n",
       "|  0.04458 |  0.02168 |  0.02878 | 0.06348  |  0.02225 |  0.06346 | -0.06591 |  0.03187 |  0.0395  | -0.0124  | -0.0407  |  0.00253 | -0.04193 |  0.02621 | -0.0024  |  0.03228 |  0.03201 | -0.0435  | \n",
       "|  0.00865 |  0.01325 |  0.02585 | 0.04855  | -0.00581 |  0.02225 |  0.00371 | -0.00174 |  0.0037  |  0.0170  | -0.0224  |  0.00790 |  0.01053 |  0.01619 | -0.0008  |  0.01107 |  0.01764 |  0.0136  | \n",
       "|  0.01507 |  0.00227 |  0.02377 | 0.00887  |  0.03258 | -0.00581 |  0.00577 |  0.06795 | -0.0037  | -0.0052  |  0.0282  | -0.00023 | -0.00601 | -0.00780 | -0.0011  |  0.00235 | -0.00524 | -0.0231  | \n",
       "| -0.00064 | -0.00924 | -0.00234 | 0.01246  | -0.05360 |  0.03258 | -0.07982 | -0.04322 |  0.0006  |  0.0102  |  0.0010  | -0.00499 | -0.01526 |  0.01826 | -0.0011  |  0.01085 | -0.02869 |  0.0362  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  V1       V2       V3       V4      V5       V6       V7       V8      \n",
       "1  0.02058  0.02058  0.00468 0.01468  0.04568  0.01745  0.02313  0.07273\n",
       "2  0.03503  0.02583  0.03903 0.03623  0.06346  0.04568  0.09344  0.13201\n",
       "3  0.04458  0.02168  0.02878 0.06348  0.02225  0.06346 -0.06591  0.03187\n",
       "4  0.00865  0.01325  0.02585 0.04855 -0.00581  0.02225  0.00371 -0.00174\n",
       "5  0.01507  0.00227  0.02377 0.00887  0.03258 -0.00581  0.00577  0.06795\n",
       "6 -0.00064 -0.00924 -0.00234 0.01246 -0.05360  0.03258 -0.07982 -0.04322\n",
       "  V9      V10     V11     V12      V13      V14      V15     V16      V17     \n",
       "1  0.0389 -0.0181 -0.0946  0.00575  0.01937  0.01868  0.0001  0.00004 -0.10389\n",
       "2  0.0397 -0.0056 -0.1147  0.00144 -0.00486  0.10639 -0.0014 -0.01039  0.00866\n",
       "3  0.0395 -0.0124 -0.0407  0.00253 -0.04193  0.02621 -0.0024  0.03228  0.03201\n",
       "4  0.0037  0.0170 -0.0224  0.00790  0.01053  0.01619 -0.0008  0.01107  0.01764\n",
       "5 -0.0037 -0.0052  0.0282 -0.00023 -0.00601 -0.00780 -0.0011  0.00235 -0.00524\n",
       "6  0.0006  0.0102  0.0010 -0.00499 -0.01526  0.01826 -0.0011  0.01085 -0.02869\n",
       "  V18    \n",
       "1 -0.0547\n",
       "2  0.0032\n",
       "3 -0.0435\n",
       "4  0.0136\n",
       "5 -0.0231\n",
       "6  0.0362"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(data_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y2 <- data_all$V2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Let create a time series object using the function “ts” from a vector - single time-series or a matrix - multivariate time-series. The data consist of the Y2 monthly returns from 1/1991 - 12/2004, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "j2 = ts(y2, frequency=12, start = c(1991, 1), end = c(2004, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.02058</li>\n",
       "\t<li>0.02583</li>\n",
       "\t<li>0.02168</li>\n",
       "\t<li>0.01325</li>\n",
       "\t<li>0.00227</li>\n",
       "\t<li>-0.00924</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.02058\n",
       "\\item 0.02583\n",
       "\\item 0.02168\n",
       "\\item 0.01325\n",
       "\\item 0.00227\n",
       "\\item -0.00924\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.02058\n",
       "2. 0.02583\n",
       "3. 0.02168\n",
       "4. 0.01325\n",
       "5. 0.00227\n",
       "6. -0.00924\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  0.02058  0.02583  0.02168  0.01325  0.00227 -0.00924"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Jan      Feb      Mar      Apr      May      Jun      Jul      Aug\n",
       "1991  0.02058  0.02583  0.02168  0.01325  0.00227 -0.00924  0.00966  0.00053\n",
       "1992  0.05392  0.02265 -0.01136  0.01804  0.01633  0.02156  0.01779  0.00341\n",
       "1993  0.02083  0.00650  0.03433  0.02154  0.02199  0.01372  0.01501  0.01853\n",
       "1994  0.02228  0.00153  0.00033 -0.00750 -0.00497 -0.00133  0.00716 -0.00250\n",
       "1995  0.00780  0.00595  0.00140  0.01080  0.00274  0.01248  0.00715  0.00886\n",
       "1996  0.01039  0.01013  0.00721  0.01611  0.01309  0.00560 -0.01023  0.01089\n",
       "1997  0.00951  0.00655 -0.01105  0.00863  0.01418  0.01499  0.01133  0.00994\n",
       "1998  0.01548  0.00946  0.01140  0.01515 -0.00118 -0.00265 -0.00933 -0.06208\n",
       "1999  0.02238 -0.00282  0.00195  0.02421  0.00782  0.00972  0.00434  0.00385\n",
       "2000  0.01347  0.00787  0.01310  0.00926  0.00210  0.01691  0.00413  0.01065\n",
       "2001  0.01624  0.00647 -0.00098  0.00436  0.00634 -0.00532  0.00405  0.00569\n",
       "2002  0.00883 -0.00108  0.00481  0.00444  0.00066 -0.00329 -0.00340  0.00543\n",
       "2003  0.00934  0.00602  0.00619  0.01297  0.00890  0.00410 -0.00039  0.00290\n",
       "2004  0.01135  0.00473  0.00353 -0.00590 -0.00428  0.00052  0.00533  0.00698\n",
       "          Sep      Oct      Nov      Dec\n",
       "1991  0.01592 -0.00923  0.00288 -0.01519\n",
       "1992  0.00102  0.00258  0.01462  0.00848\n",
       "1993  0.01092  0.01553  0.00828  0.02489\n",
       "1994 -0.00679 -0.00300 -0.00438 -0.00535\n",
       "1995  0.00950 -0.00099  0.01219  0.01217\n",
       "1996  0.00380 -0.00259  0.00593  0.01461\n",
       "1997  0.01434  0.00527  0.00874  0.00454\n",
       "1998 -0.00173 -0.00841  0.01282  0.00258\n",
       "1999  0.00078  0.00105  0.00637  0.01075\n",
       "2000  0.00393 -0.00981 -0.00618  0.00149\n",
       "2001  0.00043  0.00679  0.00392  0.00456\n",
       "2002  0.00157  0.00288  0.01018  0.00601\n",
       "2003  0.00783  0.00983  0.00404  0.01154\n",
       "2004  0.00220  0.00154  0.00888  0.00568"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "j2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we are talking about **returns** we **don't** need to take to logs and the differences of the logs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The time series plot and the histogram for the Y2 data is given by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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StVSiEpzOrV+OcfNGmih1s/egQ3N3lmZldXDuzYR+PDB8TEQHGjRbGoKLi54dGj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\nAACFINgBAAAoBMEOAABAIf4fM5MdX8jpCVwAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “Histogram of Y2”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up the graphics\n",
    "par(mfrow=c(2, 1))      \n",
    "\n",
    "plot(j2, type=\"l\", col='red',\n",
    "     lwd=1, main=\"Time Series plot of Y2\", \n",
    "     ylab=\"Monthly returns\")\n",
    "\n",
    "hist(j2, nclass=20, main=\"Histogram of Y2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The autocorrelation and partial autocorrelation plots are useful to examine if there is dependence between lagged values of the analyzed series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qqAgICsrCxq09HRMT09/ZVXXqE2T58+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WrcrLy0tISFBoJoFAYG1tjd+VAUCh/Pz8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\nsAMACISwAwAIhLADAAiEsAMACMR/AKsNpis2F3LeAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “PACF of Y2”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create Autocorrelation and partial autocorrelation plots\n",
    "par(mfrow=c(2, 2)) # set up the graphics  \n",
    "\n",
    "acf(j2, 48, main=\"ACF of Y2\")        # autocorrelation function plot \n",
    "pacf(j2, 48, main=\"PACF of Y2\")    # partial autocorrelation function \n",
    "\n",
    "acf(ts(j2, freq=1), 48, main=\"ACF of Y2\")        # autocorrelation function plot \n",
    "pacf(ts(j2, freq=1), 48, main=\"PACF of Y2\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We must note that in the autocorrelation plots presented above, the **dashed lines** are the approximate **two standard error confidence bounds** computed by ± 1,96* (1 / T), where T is the number observations.\n",
    "\n",
    "If the autocorrelation is within these bounds, it is not significantly different from zero at (approximately)\n",
    "5% level of significance.\n",
    "\n",
    "So we conclude  that:\n",
    "\n",
    "* From **ACF plot** we observe that we have **autocorrelation for lag=1 and lag=2**. We must check an autoregressive model for lag=2. **(AR(2))**\n",
    "* From **PACF plot** we observe that we also have **partial autocorrelation for lag=1**. We must check a moving average model for lag=1. **(MA(1) )**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### UNIT ROOT TESTING"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we can fit an **autoregressive time series model** to the Y2 data, by selecting the complexity of the\n",
    "model **based on AIC**. Then, we perform an **augmented Dickey-Fuller test** of unit root, based on a model\n",
    "with constant and trend "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "ar(x = j2)\n",
       "\n",
       "Coefficients:\n",
       "     1       2  \n",
       "0.2296  0.1243  \n",
       "\n",
       "Order selected 2  sigma^2 estimated as  0.0001043"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "'Order: 2'"
      ],
      "text/latex": [
       "'Order: 2'"
      ],
      "text/markdown": [
       "'Order: 2'"
      ],
      "text/plain": [
       "[1] \"Order: 2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Unit root testing for the Y1 series\n",
    "# Fits an autoregressive model, and selects the best AR order based on AIC\n",
    "m2 = ar(j2)\n",
    "m2\n",
    "paste('Order:', m2$order)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "############################################################### \n",
       "# Augmented Dickey-Fuller Test Unit Root / Cointegration Test # \n",
       "############################################################### \n",
       "\n",
       "The value of the test statistic is: -5.4669 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "############################################### \n",
       "# Augmented Dickey-Fuller Test Unit Root Test # \n",
       "############################################### \n",
       "\n",
       "Test regression none \n",
       "\n",
       "\n",
       "Call:\n",
       "lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.058347 -0.001957  0.002613  0.007711  0.058248 \n",
       "\n",
       "Coefficients:\n",
       "           Estimate Std. Error t value Pr(>|t|)    \n",
       "z.lag.1    -0.42578    0.07788  -5.467 1.68e-07 ***\n",
       "z.diff.lag -0.24318    0.07465  -3.257  0.00137 ** \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.01061 on 164 degrees of freedom\n",
       "Multiple R-squared:  0.3281,\tAdjusted R-squared:  0.3199 \n",
       "F-statistic: 40.05 on 2 and 164 DF,  p-value: 6.87e-15\n",
       "\n",
       "\n",
       "Value of test-statistic is: -5.4669 \n",
       "\n",
       "Critical values for test statistics: \n",
       "      1pct  5pct 10pct\n",
       "tau1 -2.58 -1.95 -1.62\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m21 <- ur.df(j2, type='none', lags=m2$order-1)\n",
    "m21\n",
    "summary(m21)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Model withou drift and without trend\n",
    "* The t-statistic is -5.4669 < -1.95 = Critical Value.\n",
    "* Both z.lag.1 and z.diff.lag are statistically significant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "############################################################### \n",
       "# Augmented Dickey-Fuller Test Unit Root / Cointegration Test # \n",
       "############################################################### \n",
       "\n",
       "The value of the test statistic is: -7.0302 24.731 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "############################################### \n",
       "# Augmented Dickey-Fuller Test Unit Root Test # \n",
       "############################################### \n",
       "\n",
       "Test regression drift \n",
       "\n",
       "\n",
       "Call:\n",
       "lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.063758 -0.004284 -0.000036  0.005364  0.052803 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  0.0040331  0.0009866   4.088 6.82e-05 ***\n",
       "z.lag.1     -0.6560520  0.0933188  -7.030 5.37e-11 ***\n",
       "z.diff.lag  -0.1277698  0.0766979  -1.666   0.0977 .  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.01013 on 163 degrees of freedom\n",
       "Multiple R-squared:  0.3906,\tAdjusted R-squared:  0.3831 \n",
       "F-statistic: 52.23 on 2 and 163 DF,  p-value: < 2.2e-16\n",
       "\n",
       "\n",
       "Value of test-statistic is: -7.0302 24.731 \n",
       "\n",
       "Critical values for test statistics: \n",
       "      1pct  5pct 10pct\n",
       "tau2 -3.46 -2.88 -2.57\n",
       "phi1  6.52  4.63  3.81\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Unit root testing for the Y1 series\n",
    "# Fits an autoregressive model, and selects the best AR order based on AIC\n",
    "m22 <- ur.df(j2, type=\"drift\", lags=m2$order-1)\n",
    "m22\n",
    "summary(m22)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Model with drift and without trend\n",
    "* The t-statistic is -7.0302 < -2.88 = Critical Value.\n",
    "* Both Intercept and z.lag.1 are statistically significant\n",
    "* z.diff.lag is not significant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "############################################################### \n",
       "# Augmented Dickey-Fuller Test Unit Root / Cointegration Test # \n",
       "############################################################### \n",
       "\n",
       "The value of the test statistic is: -7.2329 17.4929 26.2202 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "############################################### \n",
       "# Augmented Dickey-Fuller Test Unit Root Test # \n",
       "############################################### \n",
       "\n",
       "Test regression trend \n",
       "\n",
       "\n",
       "Call:\n",
       "lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.064083 -0.004363  0.000646  0.005553  0.050346 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  6.583e-03  1.875e-03   3.510  0.00058 ***\n",
       "z.lag.1     -6.972e-01  9.640e-02  -7.233 1.78e-11 ***\n",
       "tt          -2.706e-05  1.696e-05  -1.596  0.11243    \n",
       "z.diff.lag  -1.060e-01  7.755e-02  -1.366  0.17374    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.01009 on 162 degrees of freedom\n",
       "Multiple R-squared:    0.4,\tAdjusted R-squared:  0.3889 \n",
       "F-statistic:    36 on 3 and 162 DF,  p-value: < 2.2e-16\n",
       "\n",
       "\n",
       "Value of test-statistic is: -7.2329 17.4929 26.2202 \n",
       "\n",
       "Critical values for test statistics: \n",
       "      1pct  5pct 10pct\n",
       "tau3 -3.99 -3.43 -3.13\n",
       "phi2  6.22  4.75  4.07\n",
       "phi3  8.43  6.49  5.47\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m23 <- ur.df(j2, type=\"trend\", lags=m2$order-1)\n",
    "m23\n",
    "summary(m23)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Model with drift and trend\n",
    "* The t-statistic is -7.2329 < -3.43 = Critical Value.\n",
    "* Both Intercept and z.lag.1 are statistically significant\n",
    "* z.diff.lag and tt (trend) are not significant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We focus on the stationary time series, i.e. the monthly returns.\n",
    "We can:\n",
    "* **test for normality of Y2**\n",
    "* **create the plot of the histogram together with a density plot**\n",
    "* **also create the normal QQplot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  y2\n",
       "W = 0.88604, p-value = 1.751e-10\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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D0QKdwZnb/mreTha2T0QxyxFUUq7dUX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\nABggJAAGCAmAAUICYICQABj8A1lIoZNzACchAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Normal QQplot of Y2”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Shapiro test of normality\n",
    "shapiro.test(y2)\n",
    "\n",
    "par(mfrow=c(2,1))\n",
    "hist(y2, prob=TRUE, 50) # histogram\n",
    "lines(density(y2))\n",
    "# smooth it - ?density for details\n",
    "qqnorm(y2, main=\"Normal QQplot of Y2\") # normal Q-Q plot\n",
    "qqline(y2) # add a line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusions:\n",
    "* From Shapiro Wilk test (p-value= 1.751e-10) we **reject** the Null hypothesis for Normality.'\n",
    "* From the Histogram we see a small deviance from Normality\n",
    "* From the QQplot we see several points off the qqline.\n",
    "\n",
    "So we conclude that we **don't have Normality**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimation of ARMA models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We firstly check the moving average of lag=1 model (MA(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "arima(x = y2, order = c(0, 0, 1))\n",
       "\n",
       "Coefficients:\n",
       "         ma1  intercept\n",
       "      0.2098     0.0062\n",
       "s.e.  0.0629     0.0009\n",
       "\n",
       "sigma^2 estimated as 0.0001025:  log likelihood = 571.26,  aic = -1136.52"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ma1fit=arima(y2, order=c(0,0,1))\n",
    "ma1fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The estimated model (MA(1) can be written in the form:**\n",
    "\n",
    "$$y_{t} - 0.0084 = 0.2151* e_{t-1} + e_{t}$$\n",
    "\n",
    "**or** \n",
    "\n",
    "$$y_{t} = 0.0084 + 0.2151* e_{t-1} + e_{t}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now we will check the autoregressive of lag=1 model (AR(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "arima(x = y2, order = c(2, 0, 0))\n",
       "\n",
       "Coefficients:\n",
       "         ar1     ar2  intercept\n",
       "      0.2389  0.1228     0.0062\n",
       "s.e.  0.0739  0.0745     0.0012\n",
       "\n",
       "sigma^2 estimated as 9.919e-05:  log likelihood = 574.2,  aic = -1140.4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar2fit <- arima(y2, order=c(2,0,0))\n",
    "ar2fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The estimated model (AR(2) can be written in the form:\n",
    "\n",
    "$$y_{t} = μ*(1-φ_{1}) + φ_{1} * y_{t-1} + φ_{2} * y_{t-2} + e_{t}$$\n",
    "\n",
    "**or** \n",
    "\n",
    "$$y_{t} = 0.0062*(1- 0.2389) + 0.2389 * y_{t-1} + 0.1228 * y_{t-2} + e_{t}$$\n",
    "\n",
    "**or** \n",
    "\n",
    "$$y_{t} = 0.00471882 + 0.2389 * y_{t-1} + 0.1228 * y_{t-2} + e_{t}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lets now fit an ARMA(2,1) model. The command is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "arima(x = y2, order = c(2, 0, 1))\n",
       "\n",
       "Coefficients:\n",
       "         ar1     ar2     ma1  intercept\n",
       "      0.0060  0.1850  0.2369     0.0062\n",
       "s.e.  0.5823  0.1581  0.5915     0.0011\n",
       "\n",
       "sigma^2 estimated as 9.911e-05:  log likelihood = 574.27,  aic = -1138.53"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "arma21fit <- arima(y2, order=c(2,0,1))\n",
    "arma21fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The estimated ARMA(2, 1) model can be written in the form:\n",
    "\n",
    "\n",
    "$$y_{t} - μ = φ_{1}*(y_{t-1} -μ) + φ_{2}*(y_{t-2} -μ) + θ_{1} * e_{t-1} + e_{t}$$\n",
    "\n",
    "**or** \n",
    "\n",
    "$$y_{t} =μ +  φ_{1}*(y_{t-1} -μ) + φ_{2}*(y_{t-2} -μ) + θ_{1} * e_{t-1} + e_{t}$$\n",
    "\n",
    "**or** \n",
    "\n",
    "$$y_{t} = 0.0062 +  0.0060*(y_{t-1} -0.0062) + 0.1850*(y_{t-2} -0.0062) +0.2369 * e_{t-1} + e_{t}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summarizing we have the following:\n",
    "\n",
    "* MA(1):\n",
    "  * Variance: **0.0001025**\n",
    "  * AIC: **-1136.52**\n",
    "* AR(2): \n",
    "  * Variance: **9.919e-05**\n",
    "  * AIC: **-1140.4**\n",
    "* ARMA(2, 1)\n",
    "  * Variance: **9.919e-05**\n",
    "  * AIC: **-1138.53**\n",
    "  \n",
    "The model with the lowest variance and lower AIC score is the best. \n",
    "Here the AR(2) model fits better that any of the other 2 models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diagnostic plots\n",
    "\n",
    "Now we will provide some **diagnostic plots** for the **residuals** of the above models.\n",
    "Based on the residuals of the AR(2) model, we will present the:\n",
    "* autocorrelation **(acf)** plots and the partial autocorrelation **(pacf)** plots of the **estimated residuals**\n",
    "* the autocorrelation plots and the partial autocorrelation plots of the **squared** residuals (check **heteroskedasticity**)\n",
    "* normality plots (examine the assumption of **normality of residuals**)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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MDnn3+u+kwAAJTKw8PDw8OD6ywAOPbJ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\nAEBHINgBAAAA6AgEOwAAAAAd8f8AQi2f4Bs4qCkAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “Normal QQplot of residuals”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar2residuals <- ar2fit$residuals\n",
    "residuals <- ts(ar2residuals, frequency=12, start = c(1991, 1), end = c(2004, 12))\n",
    "\n",
    "par(mfrow=c(3,2))\n",
    "\n",
    "# set up the graphics\n",
    "acf(ts(residuals,freq=1), 48, main=\"ACF of residuals\")\n",
    "pacf(ts(residuals,freq=1), 48, main=\"PACF of residuals\")\n",
    "acf(ts(residuals^2,freq=1), 48, main=\"ACF of squared residuals\")\n",
    "pacf(ts(residuals^2,freq=1), 48, main=\"PACF of squared residuals\")\n",
    "qqnorm(residuals,main=\"Normal QQplot of residuals\")\n",
    "qqline(residuals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Based on the residual plots presented above, it seems that the assumptions with respect to the residuals\n",
    "are satisfied, thus the autoregressive AR(2) models is a appropriate candidate model for modeling the\n",
    "stationary series of Y2. Obviously, other alternative model specifications can be used.**"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R [conda env:mro_env]",
   "language": "R",
   "name": "conda-env-mro_env-r"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}