Time_Series_Assignment_Variable_Y1_ARMA_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time Series and Forecasting\tAssignment\n",
    "\n",
    "### Course:\tTime Series\tand\tforecasting\tmethods\n",
    "#### Program: MSc in Data Science (part-time)\n",
    "\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": 4,
   "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": 5,
   "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/george/AUEB/TimeSeries/time_series_in_r/Data-Assignment-Feb-2018.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1 <- data_all$V1"
   ]
  },
  {
   "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 Y1 monthly returns from 1/1991 - 12/2004, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Jan      Feb      Mar      Apr      May      Jun      Jul      Aug\n",
       "1991  0.02058  0.03503  0.04458  0.00865  0.01507 -0.00064  0.02146  0.01603\n",
       "1992  0.03512  0.01805  0.00244 -0.00016  0.01523 -0.00714  0.01809 -0.00539\n",
       "1993  0.02073  0.01090  0.02813  0.01244  0.02339  0.02362  0.01831  0.02673\n",
       "1994  0.02248 -0.00837 -0.01808 -0.00920  0.00323 -0.00083  0.00986  0.02070\n",
       "1995 -0.00720  0.00815  0.01160  0.01610  0.01214  0.02008  0.02735  0.01746\n",
       "1996  0.02469  0.00813  0.01031  0.03531  0.02619 -0.00250 -0.02523  0.01839\n",
       "1997  0.02741  0.00595 -0.02085 -0.00547  0.03968  0.02269  0.03433 -0.00096\n",
       "1998 -0.01142  0.02826  0.02570  0.00545 -0.02498 -0.00555 -0.01213 -0.09108\n",
       "1999  0.01868 -0.01712  0.02765  0.04121  0.00332  0.03232  0.00124 -0.00425\n",
       "2000  0.00167  0.05677  0.00440 -0.03334 -0.02430  0.03191 -0.01117  0.03285\n",
       "2001  0.02974 -0.02613 -0.01948  0.01626  0.00894 -0.00012 -0.01125 -0.00691\n",
       "2002  0.00303 -0.00848  0.01761  0.00134 -0.00104 -0.02079 -0.03000  0.00393\n",
       "2003  0.00554 -0.00078  0.00049  0.02547  0.03490  0.01280  0.01221  0.01750\n",
       "2004  0.01905  0.01113  0.00433 -0.01560 -0.00398  0.00642 -0.01078 -0.00013\n",
       "          Sep      Oct      Nov      Dec\n",
       "1991  0.01882  0.01418 -0.00103  0.03621\n",
       "1992  0.01712  0.01858  0.02522  0.02268\n",
       "1993  0.01332  0.02923 -0.00112  0.03659\n",
       "1994  0.00491 -0.00460 -0.01748 -0.00555\n",
       "1995  0.01510 -0.01109  0.01429  0.01657\n",
       "1996  0.01650  0.00551  0.01653  0.00901\n",
       "1997  0.03294 -0.01963 -0.01366  0.00434\n",
       "1998  0.00327  0.00859  0.03332  0.02418\n",
       "1999 -0.00242  0.01175  0.04617  0.07215\n",
       "2000 -0.01758 -0.02321 -0.04008  0.01579\n",
       "2001 -0.03028  0.01839  0.01922  0.01566\n",
       "2002 -0.01673  0.00468  0.02018 -0.00309\n",
       "2003  0.01083  0.02373  0.00984  0.01794\n",
       "2004  0.01510  0.00684  0.02658  0.01468"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "j1 = ts(y1, frequency=12, start = c(1991, 1), end = c(2004, 12))\n",
    "j1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note:\n",
    "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": [
    "### Methodology\n",
    "\n",
    "In order to work we will use the **Box-Jenkins methodology** that constists of the following steps:\n",
    "* **Identification step**\n",
    "  * Use autocorrelation and partial autocorrelation of the series to find out appropriate values of p and q\n",
    "* **Estimation step**\n",
    "  * Estimate the models parameters using Maximum Likelihood method and least squares method\n",
    "* **Diagnostic checking step**\n",
    "  * Examine if the chosen (estimated) model fits the data reasonable well - test if the residuals of the estimated model are uncorrelated, homoscedastic and normal, i.e. white noise\n",
    "* **Forecasting step**\n",
    "  * Compute forecasts based on the fitted model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The time series plot and the histogram for the Y1 data is given by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tGjRxKJxN3dvQnvPHH5Mqqq0KeP4kjDBLtOneRfR0VhxQpUVcHWtn7vtJHLyYGV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M4OBgO9fQtJycnCtXroSEhLDcCQA3pm+x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",
      "text/plain": [
       "Plot with title “Histogram of Y1”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up the graphics\n",
    "par(mfrow=c(2, 1))      \n",
    "plot(j1, type=\"l\", col='red', lwd=1, main=\"Time Series plot of Y1\", ylab=\"Monthly returns\")\n",
    "hist(j1, nclass=20, main=\"Histogram of Y1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note:\n",
    "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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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esWM1WhUFhdXS3zzdfV1WVG6uvrf/vtt7a2NuYnByMjo9raWuZmDQ0Nenp6zEh7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6oxzBQNczbJ/kp1ienp6fffZZY2Pj8ePH\nBQJBWVkZ2xl1yZIlS5gXjvX+V3Hp0iVjY+MHDx5k/620tJRShcwzMzMNDAyOHj1aXV194cIF\nAwODa9euUaqQ+ZMnT/L/NmnSpNDQ0KKiIkoVMofnp7qfssoNbpQqj2801R3lKAx0PcLxwi4/\nP3/ixInGxsbu7u5Xr15lO52ukhn7ev+rkM4tJDV16lRKFTKnKOrSpUve3t4CgcDFxeXXX3+l\ngyqRudTUqVOlswCoVubQM6r7Kavc4Eap+PhG48AoR2Gg6zIeRVHK2jkIAAAAAArE5XPsAAAA\nANQKCjsAAAAAjkBhBwAAAMARKOwAAAAAOAKFHQAAAABHoLADAAAA4AgUdgAAAAAcgcIOAAAA\ngCNQ2AEAAABwBAo7AAAAAI5AYQcAAADAESjsAAAAADgChR0AAAAAR6CwAwAAAOAIFHYAAAAA\nHIHCDgAAAIAjUNgBAAAAcAQKOwAAAACOQGEHAAAAwBEo7AAAAAA4AoUdAAAAAEegsINewcTE\n5OLFi2xnAQCgWBjrQNFQ2AEAAABwBAo76L1Onjzp5uamr69vZWX15Zdf0sHffvvN3d3d1NR0\nwYIF77///rfffstukgAAzwljHcgRCjvoperr62fOnBkcHFxUVHTo0KHNmzenp6cXFBRMmTJl\n1apV2dnZXl5e4eHhbKcJAPBcMNaBfGmynQBAx3R0dNLT0wcNGkRRlImJia6ublVV1fnz5ydM\nmDBjxgxCyIcffrh792620wQAeC4Y60C+UNhBL6WhoXH27NmYmJi2trYhQ4ZoaWkRQnJzcwcO\nHChtY2dnx1p+AADygLEO5AuFHfRSFy5c2LBhQ1JSEj2iXbp0iRBiaWl548YNaZucnBy20gMA\nkAuMdSBfOMcOeou6urpqhvLycl1dXUNDQ4lEsm3btvz8fLFYPGPGjMuXL8fGxtbW1v74448Z\nGRlsZw0A0D0Y60ChUNhBbxEYGGjMMGXKFB8fn4EDBw4bNqy1tXXFihWzZ88WCoXR0dGrV6+2\nt7fPysqaNGmSQCBgO3EAgG7AWAcKhUOx0CtUVla2D0ZFRTGffvvttyKRiKKoe/fu0REvLy+h\nUKiM/AAA5AFjHSga9tiBKmlubg4MDLx9+zYh5PTp0w8fPpwwYQLbSQEAyBnGOugx7LEDVeLs\n7Lxv376ZM2fW1NTY2trGxsYaGxuznRQAgJxhrIMe41EUxXYOAAAAACAHOBQLAAAAwBEo7AAA\nAAA4AoUdAAAAAEegsAMAAADgCBR2AAAAAByBwg4AAACAI1DYAQAAAHAECjsAAAAAjkBhBwAA\nAMARKOwAAAAAOAKFHQAAAABHoLADAAAA4AgUdgAAAAAcgcIOAAAAgCNQ2AEAAABwBAo7AAAA\nAI5AYQcAAADAESjsAAAAADgChR0AAAAAR6CwAwAAAOAIFHYAAAAAHIHCDgAAAIAjUNgBAAAA\ncAQKOwAAAACOQGEHAAAAwBEo7AAAAAA4AoUdAAAAAEegsAMAAADgCBR2AAAAAByBwg4AAACA\nI1DYAQAAAHAECjsAAAAAjkBhBwAAAMARKOwAAAAAOAKFHQAAAABHoLADAAAA4AgUdgAAAAAc\ngcIOAAAAgCNQ2CnJrFmzeDwej8c7ffp0+6WHDh3y8/Pr37+/kZHRiy+++NNPP7W1tdGLhg0b\nxuvIxYsXu5VAUVHRmDFjdHR0HB0d5fB62BMSEsLj8ebNm/ec/fz666/r1q2Lj4+XS1aK8LSP\n7NixY/R34MyZM9LgRx99xOPx9PX1S0pKmI0DAwO1tLSUlDGoDS8vL+Zw1KdPn5EjRx48eLB9\nSwx98oKhD0NfV1GgePX19X369KHf8Llz5zIXtbW1BQUFtf9cpk6d2traSlGUq6trhx/chQsX\nupXDunXrCCH6+vpBQUHyfG1Kt2TJkvZvYw9MnTqVEPLZZ5/JJStFeNpH1tbW5u7uTgh5+eWX\n6UhdXZ2RkREhZOnSpcyWJ0+e1NTU1NTUVF7SoB48PT07HJciIiKYzTD0yRGGPgx9XYQ9dspw\n+vTp+vp6+vGpU6eampqkiyIjI6Oioggh8+bNu3HjRmpqamhoKCHkxIkTzJ+/S5curftfr776\nardyKCsrI4S8+eabhw8ffv5XBErwtI+Mx+PRA9+VK1fu3LlDCDl8+HB1dbW2tjb95SGErFq1\navz48VOmTGltbVV64qAuFi9eXFdXV1tbm5yc7OLiQgj59ttvmQ0w9EEPYOh7XmxXlmqB/oXk\n5+fH5/MJIadOnZIuGjBgAL2I2X7ixImEkClTplB//2xduXJlVzYUHR3t7e1tZGRkb28/a9as\nnJwcOj569GjpJy4QCGTWys3NnTdvnpWVlb6+vqur63fffUf/YqYoqqWl5fPPP7e3t7ezs9u6\ndWtwcDAhZMGCBRRFlZeX0x1mZmbSjefOnUsIWbJkCf00Kytr5syZlpaWurq6jo6OX375ZUtL\nC72IXvHatWvvv/++p6cnRVFNTU2fffbZkCFD+vTp4+npGR0dLU1PIpGsXbt20KBBlpaWoaGh\nH3zwAXnKz9aud8t8Q8aMGfPM19K+Zzpy/vz56dOnm5mZ2dnZ/fvf/+7KWyqXj4yiKA8PD0LI\nvHnzKIpyc3MjhCxevFi61NzcXLq62v5sBcWh99hJ/0Aoitq1axchRFdXt62tTRrE0IehD0Of\n8qGwU7jq6modHR1CyLFjx8aMGcP8y6R/lxBCzpw5w1ylpqYmPz+/pKSE+nt0k/nZ2tjY2H5D\nGzdupHszMTHR1NQkhBgZGeXl5VEUtWvXrpEjRxJCXFxcvvzyS+ZaEomE/qmtq6trbW1N97B6\n9Wp66fz58+mItrY2IaR///5dHN2ampqcnZ0JIXw+X/qX9tVXX9Et6aeTJk0ihDg4OFAU5efn\nRwjR0tIaOnQoj8cjhOzevZtuTA+p0hzoIzudjG5d6XbXrl302RujR4/evXt3F0c3Zs90pG/f\nvnS3tLNnzz7zLX3+j4x29uxZ+qX9+uuvhBANDY3Hjx/LtLl+/bo6j26gOO0Lux9//JEQYmxs\nLI1g6MPQh6GPFSjsFC4iIoL+y6ytrd2yZQshxNDQkB6eEhMT6S/3o0ePnrZ6hyeaLFq0SKZZ\nUVGRnp4eIWTDhg0URRUXFw8dOpQQsnDhQrrB087PuHfvHt2nSCSiKCo8PJwQYm1tTVHU3bt3\n6T/dffv2SSSSo0eP0i27MrrRf1cCgaCoqIiiqE8++YQQMn78eLolvaKlpeWePXsuX75Mn8Zr\naGhYXFxMUdS+ffvov/PW1taMjAwNDQ1CyJ49eyQSSWxsLJ1SJ6NbV7ql/vdEky6ObtKepRF/\nf/+qqqqHDx/Soxh9nkcnb6lcPjKpF154gRBCd0L/fpWh5qMbKA5d2EkPxaamptIj1dixY6Vt\nMPRRGPow9LEB59gpXHR0NCFkwoQJAoHgzTffJITU1NRcunSJEEL9/UdC/wE/j1u3bjU0NAiF\nws8//5wQYmFhQQ8o9Pe7E0ZGRvTWJ0yYEBoaOnDgwObm5ry8PELItWvXKIoaPnz422+/zefz\n33rrLfpnd1eMGjWqqqoqIyMjLS1t06ZNMTExhJC6ujpmm82bN7/33nuvvPLKtWvX6Jx/+OGH\nzz//PCUlhRBSXV2dnZ2dkJAgkUiGDBny3nvv8fn8adOmjRs3rvNNd6XbLr6Kp/UsjSxbtszI\nyMjR0fG1114jhJSWlpJO31KmHn9kUuvXryeENDQ08Pl8uhMAZfrpp58EAoGBgcHw4cPT0tII\nIczvIYY+DH0Y+liBwk6xnjx5cvnyZULIq6++Wl9fb21tbW9vTwih/9ql13I/fvyYuVZGRsbJ\nkyevXLkijcicaPLzzz/LbCg3N5cQYmtrKx0oBw0aRAjJycnpPENLS8tTp065u7uLRKJvvvlm\nwoQJVlZWkZGRhBD6D3LgwIHSxnSfXcHn8z/99FM7OztfX9/NmzfTR2RkODg40A/oJB89erR5\n8+bNmzdv376djmdmZtKvi7ndZ+bQlW67+Cqe1rOU9Io/gUAgDXbyljL1+COTmjhxIn2KycSJ\nE4cMGdLt1wMgJ1paWu7u7seOHaP/mScY+jD0YehjDwo7xTp27FhLSwshZOXKlfRPW5FIRP6+\nQEwoFNL7seld5VIff/zx1KlT9+7d2/UN2djYEEJyc3MlEgkdoUdMOt45Pz+/O3fuPHjw4N//\n/vfIkSPLysoWLVpUU1NjZWVFCKETpjEfSzU0NNAPpJe/EUKioqL27t1ramr6+++/V1dXh4SE\ntF+RPp+aEGJhYUEImT59usz+5EmTJtHvzzNz6G63T1u3w9fSvudnetpbymzzPB+ZlFAoJIQw\nzxcGUBrpAbvm5uY7d+4EBARIF2How9CHoY8tKOwUiz4Y0Z70kAR98XZ0dPTy5cvv3bv3+PHj\nVatW0SeHTpkypesb8vT01NXVLSsr27p1KyGktLSUfvDMIwi7du0yMDBwc3OztbVduXIlPQFB\nc3NzSUkJvW5KSsovv/xCUdSxY8foPfw0Q0ND+vdWREREY2PjjRs34uLipEvv379PCLGwsBg1\nalRDQ8PT3gfaqFGjCCEJCQn0CR/x8fGOjo7Dhw+vra318fHh8Xjp6enh4eEURcn8mu9cJ91K\n29CHSDp/Ld3VyVvKbNbjjwyg98PQh6EPQx9rundKHnRHcXEx/Tfz448/SoNtbW30IQn6zFCJ\nRDJ9+vT2n4t0YsauX/O/YcMGel1zc3N6xm1jY2P6OiPq6aejPn782NDQkBCio6Pj7OxMr+jl\n5UUvnTZtGt0nfVkW/UOQPoOYoqiXX36ZXkr/nqP3ydM/4ukDLoQQIyMjgUBAN3Bzc6NXpBfd\nuHFD+p68+OKLdONhw4bRjbdu3UovnTVrFjMHemknZxB3seRdjy4AACAASURBVNvFixcTQvr0\n6fPBBx90/lra99w+smzZMkLIrFmznvmWPv9HxkTP6fW0Nmp+BjEoTvurYpkw9GHow9DHIuyx\nU6D//Oc/EolEV1d39uzZ0iCPx1u4cCH5+5AEn8+PiYnZt2+fr6+vubl53759fXx8Dh8+fOjQ\noe5ubvXq1YcPHx49enRzc7OlpeXs2bNTU1Ol15w/zcCBA69cuRIQEGBubp6dnd2/f/93331X\nevOf6OjoFStWDBgwoH///ps2bZIOdrQDBw689tprBgYGDg4O33zzDfN3dmBg4JdffknP5BQY\nGHjy5ElCyP379x88eNA+Bx6PFxcXFxISYm5unpWVNXLkyCNHjkgnnIyMjPzss88GDhxobGy8\naNEi+t3ris67XbFixYgRIyQSCT3zQievpbs6f0uZevaRAfRyGPow9GHoYxGP+rsAB3im999/\nf8+ePQsWLDhw4ADbuQAAKAmGPlAh2GMHAAAAwBEo7AAAAAA4AoUdAAAAAEfgHDsAAAAAjsAe\nOwAAAACOQGEHAAAAwBEo7AAAAAA4AoUdAAAAAEegsAMAAADgCBR2AAAAAByBwg4AAACAI1DY\nAQAAAHAECjsAAAAAjkBhBwAAAMARKOwAAAAAOAKFHQAAAABHoLADAAAA4AgUdgAAAAAcgcIO\nAAAAgCNQ2AEAAABwBAo7AAAAAI5AYQcAAADAESjsAAAAADgChR0AAAAAR6CwAwAAAOAIFHYA\nAAAAHIHCDgAAAIAjUNgBAAAAcAQKOwAAAACOQGEHAAAAwBGabCfwvCIjI0+fPs12FgDQc3w+\nPywsbPDgwWwn0qthrANQdcoZ61S+sDtx4sTDhw+9vb3ZTgQAeujw4cOTJ09GYdc5jHUAqk45\nY53KF3aEkAkTJmzbto3tLACgh86dO8d2CqoBYx2ASlPOWIdz7AAAAAA4AoUdAAAAAEeozKHY\nY8eO7dmzp3385s2bzs7Ona/7ww8/uLu7jx8/XiGZAQBAr/fLL7+YmJhMmTKF7UQAFEtlCrt+\n/fp5eHi0j9+4caOqqqrzdWNjY2tra1HYAYDSUBT1448/Xr582dvb+9133zU2NiaElJWVLV68\n+Pjx42xnp47Onj3br18/FHbAeSpT2L300ksvvfRS+3hkZKS+vr7y8wEA6MSGDRt+/vnnt99+\n+/z585cuXbpw4YKGhoZYLD5x4gTbqQEAl+EcOwAA+fv555+PHz++bt26y5cva2ho/Pvf/2Y7\nIwBQCyjsAADkr6amxsHBgRDC5/N//PHHbdu2lZeXs50UAHAfCjsAAPkbOXLk999/39bWRggZ\nOHDgokWLFixY0NjYyHZeAMBxKOwAAORvx44dO3fuNDIyys3NJYSsXr2aEDJ69Gi28wIAjlOZ\niycAAFSIq6trTk7OjRs3TE1NCSE6OjqnT5++fPnyzZs32U4NALgMhR0AgEIIBIJXX31V+pTH\n4/n6+vr6+rKYEgBwHg7FAgAoSUpKypo1azpv891335l25OTJk+fPn1dOngCgurDHDgBASXJz\nc48ePbphw4ZO2kyfPt3GxqZ9PDg4WFtbW2GpAQBHoLADAFASf39/f3//ztvY2Nh0WNgtW7ZM\nUxMjNgA8A4YJAACFKC8vj4yMFIlEpaWlZmZmTk5Oc+bMMTc3ZzsvAOAynGMHACB/cXFx9vb2\nx44doyjKwcGBz+fHxsba29tfu3aN7dQAgMtY2GN348aNzMzM1157TV9f/+uvv05OTvbz83v/\n/feVnwkAgIKsXLly586d8+fPZwZjY2OXLVv2119/sZUVAHCesgu7n3/+ecWKFXw+387ObuLE\nibq6usOHD1+zZk1dXV1oaKiSkwEAUBCRSOTn5ycT9PPzW7RoESv5AICaUHZht2XLlrNnz/bp\n08fT0zM8PNzLy4sQ8uqrry5evBiFHQBwhre3d1hY2JYtWwQCAR0Ri8Xr168fNWoUu4kBALcp\nu7ArKChwcXHR19fn8/nu7u50cMSIEcXFxUrOBABAcfbs2RMUFGRubu7o6GhkZFRbW/vo0SMX\nF5cTJ06wnRoAcJmyCzsnJ6fo6GiBQEBR1K+//jp37lxCSHR0tJubm5IzAQBQHDs7u8TExJSU\nlMzMTOlVsdJfswAACqLswm7dunWBgYGGhob//e9/Z8yY8dNPP7W1td29e/fChQtKzgQAQNHc\n3Nzwq1X5KIqaNm3a9u3bbW1t2c4FQNmUXdhNnTq1uLhYX19fX1//9u3bZ8+ebW1t9ff3t7a2\nVnImAADASW1tbSdPnvz4449R2IEaYmG6E+n8nJaWlu+++24X12ppacnLy2sfl0gkcssMAAAA\nQJX1ijtPpKSkPPP+iRs2bHhaAz4f0ywDAAAA9I7Cris3xl61atWCBQvax729vYVCoaIyAwDo\nHShKr7nZOivrn4iVFdHR+f/HYjGRmVpAzZcSMrCwUFf6dllZ/dOy1+aMpZxf2tpqTVFE4SgV\nZ2lp6ebm1nkbHx+f9evXKycfAOgua2vryMhItrPo7fr0iSCEYv63ceM/S99/n8JSqeDgtvZL\nAwMDlyxZ0mtzxlI1WfrZZ5cpBeNRyqge/4d8b4xtZWUlFAqTk5M7aTN27FhfX981a9b0bBMA\noFA2NjZff/01PfkRPI2lpb2xscuZM2fopzwesbEhmn8fdGlqIgUF/zRW86VisaRPH6fo6Gh6\nDnx66ezZ0/v167djx47emTOWqsPSMWNGb926RNFjnbIPxcbFxQUEBLi5uY0YMcLBwaG6ujo2\nNnb16tXnzp3z8fFRcjIAAKqCx2vW1s4fOLDjpTo65GmL1HMpIVmWlo0dtum1OWMp55dqaBQ8\ntYX8KLuww42xAQAAABRE2deTPu3G2CKRSMmZAAAAAHCMsgs7+sbYdXV10ohYLA4LC8ONsQFA\nmebNmycdiDAdphxduXJlxowZbGcBoL6UXdjt2bPnzp075ubmw4YNGzNmjJubm7m5eXx8/L59\n+5ScCQCos0OHDjU1NdGPzc3Nc3Jy2M2HM7Kysm7fvs12FgDqS9nn2OHG2AAAAM/vnXfeCQ0N\nHTx4MNuJQO/CzgTFuDE2AADA84iNjfX390dhBzJ6xZ0nAAA4JiQk5GmLduzYocxMAECtoLAD\nADUVHh4uEAgIIU1NTREREWZmZnT8ww8/fP7OR44c+cknn1hYWLz88svP3xsAQBehsAMAdeTu\n7h4dHU0/dnZ2Pn78uHSRXAq7hQsXikSisrIy7J8DAGVCYQcA6ujOnTuK3kRAQADmXQcAJUNh\nBwCgEO7u7rjkHwCUTNnz2AEA9BK3b98OCwujHx88ePCtt966ceMGqxkBADwv7LEDAHUUHx//\nxhtvBAQE0E89PDwuXrw4duzYixcvKu5yh5SUlKNHj27YsKGTNufPnz9w4ED7eGVlpZ6enoIS\nAwDOwB47AFBHYWFhq1atioqKop+6uLgcPnw4NDS086rrOeXm5h49erTzNpqamiYd4fMxXAPA\ns2GPHQCoo9TU1PDwcJlgUFDQ3r17FbdRf39/f3//ztv4+vr6+vq2j585c4aenAUAoBMo7ABA\nHeno6LQPampqUhQlr02Ul5dHRkaKRCLp7RPnzJljbm4ur/67qLW1VVMTQz2AulCZv/abN2/G\nxsa2j9fU1OBXLAB017Bhw86dO+fs7MwMnjx5cujQoXLpPy4uLiAgwM3NbcSIEQ4ODtXV1bGx\nsatXrz537pyPj49cNtEVhw8f3rNnz7Vr15S2RQBgl8oUdllZWR3OCNXS0tLc3Kz8fABApa1d\nu/b11183MDCYP3++lpZWc3PzgQMH1q5de+LECbn0v3Llyp07d86fP58ZjI2NXbZsmTInt6us\nrKyqqlLa5gCAdSpT2M2aNWvWrFnt41ZWVkZGRsrPBwBU2tixY2NiYoKDg4ODgy0sLEpKSszM\nzKKjoydNmiSX/kUikZ+fn0zQz89v0aJFculf1X3xxRcODg4LFy5kOxEArlGZwg4AQL7eeOON\nrKysjIyMzMxMe3v7IUOGaGtry6tzb2/vsLCwLVu2SM8VEYvF69evHzVqlLw2odJSUlJaWlrY\nzgKAg1DYAYD60tLScnV1dXV1pZ+Wl5dHRUUtXbr0+Xves2dPUFCQubm5o6OjkZFRbW3to0eP\nXFxc5HWoFwCgQyjsAEDdtba20tMCnzlzxtTUVC6FnZ2dXWJiYkpKSmZmpvSqWNxhDEDuGhoa\ndu/evXz5ch6Px3YuvQIKOwBQX3fv3o2IiIiMjCwtLV2wYMGFCxfGjRsnx/7d3Nzc3Nzk2CEA\nyHj48OHHH3+8cOFCExMTtnPpFWSnMp83b15dXR39WCKRKD0fAABl2LVrl5eXl4eHR1ZWVnh4\nuFAo3Lx584QJEzQ0NNhODQCg52QLu0OHDjU1NdGPzc3Nc3JylJ4SAIDCLVmyxNjYODc3NzY2\n1t/fH/Uc61JSUkJDQ9nOAkDl4eaDAKCOPv300/T0dC8vr3Xr1uXn57OdjvI0NTW9+eabT548\n6e6KLS0tgYGBFRUVisiKEJKSkhITE6OgzrvuX//6V25uLttZAPQcCjsAUEebN2/Oy8vbvXt3\nSkqKo6NjaWlpVFSU4qqW3qOmpub06dNFRUXdXbGuru7YsWOcL4IPHz6cmZnJdhYAPYfCDgDU\nlIaGxuTJk2NjY3Nzc7/55pv9+/f379/f39+f7bwAAHqug6tiw8PD6Rk1m5qaIiIizMzM6PiH\nH36o1NQAAJRCKBQuX758+fLlSUlJ+/fvZzsdAICeky3s3N3do6Oj6cfOzs7Hjx+XLkJhBwDc\n5uXl5eXlxXYWAAA9J1vY3blzR8kZjBo16tSpU/369VPydgEAQOUcO3bMzMxs/PjxbCcC0Esp\ne4LijRs3ykTS09O/++47IyOjL774QsnJAACAajl06JCdnR0KO4Cn6aCwu3379qlTp8LCwggh\nBw8ePHnyZGho6OjRo+WyvatXr8bFxY0bN046Q3Rra2tqaqqenp5c+gcAAABQW7JXxcbHx3t7\nez98+JB+6uHhoaurO3bs2CtXrshlexcvXty6dWtBQcGKFSuOHz9+/PhxQ0PDffv2MU/mAwAA\nAIAekC3swsLCVq1aFRUVRT91cXE5fPhwaGjohg0b5LI9Ho8XGhp65MiRxYsXr1mzprW1VS7d\nAgB0C+/p2E4NOOKPP/74888/2c4C1I7sodjU1NTw8HCZYFBQ0N69e+W4VU9Pz6SkpJCQkDFj\nxjQ0NMixZwCArnjaRLu1tbVKzgS4as+ePZqami+88ILStkhRFEVRfD5mqFVrsoWdjo5OB400\nNSmKku+GBQLBgQMHYmJizp8/r6+vL9/OAQA6Z2VlRT9IT0+vqqqiH4vF4qCgoLKyMvbyAui5\nVatW1dTU7Nq1i+1EgE2yhd2wYcPOnTvn7OzMDJ48eXLo0KGK2PyMGTNmzJihiJ4BAJ5pzZo1\nW7Zs0dXV1dLS0tfXz8/P//jjj9lOClSSh4fHgQMHhg8fzmIOlZWVNTU1LCYAvYHsDtu1a9eu\nXr06PDy8paWFENLc3Lx37146qLgkUlJS1qxZ03mbH374wbQjxcXF6nB7RwBQhPDw8EuXLl29\nenXatGl5eXnff/+9paUl20mBSkpPT+/BHXgB5E52j93YsWNjYmKCg4ODg4MtLCxKSkrMzMyi\no6MnTZqkuCRyc3OPHj3a+fUZAQEB0kMnTMHBwYaGhgpLDQC4rKqqasSIEYaGhvfv3yeEhISE\nDB8+fMWKFWznBSA3+fn51tbWbGcBytPBPHZvvPFGVlZWRkZGZmamvb39kCFDtLW1FZqEv7//\nM2+8bWtra2tr2z6+bNkyLS0txeQFABzn5OR05MiR4OBgQkh2drahoWFhYSHbSQHIze+//+7r\n6ysWi9lOBJSn4ztPaGlpubq6urq60k/Ly8ujoqKWLl0ql02Wl5dHRkaKRKLS0lIzMzMnJ6c5\nc+aYm5vLpXMAgK5bv379zJkzfX19Z86c6eXlpaOj4+fnx3ZSAHLT1NTU1NTEdhagVJ3dUqy1\ntfX8+fMHDhw4c+aMqampXAq7uLi4gIAANze3ESNGODg4VFdXx8bGrl69+ty5cz4+Ps/fPwBA\n102ZMqWiokJHRyckJMTR0bG8vHzmzJnspiQSiW7dutU+Xl9fz+fz//Of/3Sybk5OjrGxsZGR\nkTRy586d6upq5lr0yfUXL168d++eNHjz5s2+ffva2dkxN1dcXDxo0CBmhBASFxcnncGeEJKX\nlycQCKR3EiKE3Lp1q66uTibPtLS0oUOHMqfhKCoq0tDQYDa7efOmWCyWWTE9PX3w4MEaGhrS\nSEFBQUtLC7NZY2Njbm6uk5OTNNLW1kYIuXLlSnFxsTSYn58vk1hTU1N2drbMxYIURV29epV5\n6nZRUZGmpqZQKGSuKBKJBg8ezFyxra3t2rVrzGsXcnJyZD6ylpaWzMzMIUOGMFe8f//+oEGD\nmEfGSkpKCCEWFhadr9jS0pKYmEifEE/LysqSeQ/T0tIoipJ5VzMyMuzs7JiTYJSVlbW0tDBP\nMJVIJA8ePHBxcWGu+PDhQ1tbW11dXWmkoqKisbGReaJUhys+evTI2tqaeYupioqKhoYG5jHi\ntra2e/fuSfcoSVe0srJiTp1RWVlZV1dnY2MjjeTk5BBCTp482adPH2nw8ePH/fr1Y0aqqqpq\namqYh/4oikpLSxs2bBhzi48fP7awsBAIBNJIdXV1VVXVgAEDOl9RJBKZm5sbGBiQp2toaGhs\nbOykgVzwOpzH5O7duxEREZGRkaWlpQsWLJg3b964ceOYf1o95ubmtmLFivnz5zODsbGxGzdu\n/Ouvv3rQoZWVlVAoTE5O7qTN2LFjfX19n3l9BgCwwsbG5uuvv547dy7bifQK27dv37ZtW/t4\ndnY2n8/v8IwUqcLCQn19fWNjY2lELBbX1dX17dtXGqEoqrCwsF+/fswhna5umf+Y1dbWVldX\nM//d7XDF4uJiHR0dZmHX0NBQU1PDLEooihKJRFZWVsxK4smTJ1paWsx/BRsbG6urq5+5YmVl\npYaGBvPU6vr6+oqKCpl3prCwUCgUMk/U6XDF8vJy5j/YHa5YWlrK5/OZh5XEYnFpaSmzDqZX\nNDc3Z9ZnVVVVPB6PWWd3uGJ2dnbfvn2ZtQs94Q6zlGxoaCguLra3t2euWFRUZGpqynxzqqur\nKYpifgFaWlrKyspkLgnKyckxNzdnFj0VFRWtra3MN7+xsbGwsHDgwIHMFXNzc01NTZnfk/Yr\nNjU1FRQU2NvbM+f6br/ikydPmpub+/Xr1/mKeXl5xsbGzO9JZWVlU1MTc0WJRFJcXGxpaclc\nMT8/38jISGbFxsbG/v37M9+cvLw8Ozs75k+O/Px8Q0ND5vekqqpKLBYz30N6xQEDBsj85BAI\nBMyPu73c3NwvvviCvmWrAlH/a+fOnZ6enlpaWtOmTTt16pRQKCwuLqbkx8DAoLS0VCbY0NBg\nYmLSsw4tLS3d3Nw6b+Pj47N+/fqe9Q8AimZtbR0ZGankjWpqakZERGh2RMmZdFFXxrpvvvkm\nPj5eLptLTExcuXLlM5tNnDhx1apVnbcRi8U8Hu/27dvdzYHet/F/7d15WBNnHgfw4ZLDcCcC\nAgGUQ0EFLKjQqvVAV9RFEcW7xePRrmDVtegWFSttle7WrrYq64PWa3WX9SwKAqIrWC88QEGL\nIuG2codwkzD7R7pxisoRkkxm+H6e/kF+M0y+IfT1x2TmfW/evNn5bidPnrSysurpwUmSjIuL\n4/F4Xe62YMGCVatWUSvnz583MTGR4xkvXrzYv3//DkUOhxMfH0+tLFu2bOnSpdTK5cuXdXV1\n5XjGt+LxeHFxcdRKaGhoUFAQtZKWlkYQhFgsphYHDhz4z3/+k1pZv359QEAAtXLr1i2CIJqa\nmqhFPp9/9OhRauWzzz6bPn06tZKRkUEQhEgkohYHDx4cGxtLrXz++edTpkzp/AWSJBkVFdXh\nVy4yMnLChAnUikQiuXTpUodvHD58+N69ezsc6oMPPqBWcnNzpZ0ctejj43PgwIHOU6lmrOv4\nUWxoaOjkyZOLioqk7bBCztJR+fr6bt++PTo6Wta5NzY27tixY9SoUYp9IgCATuTl5XG53EmT\nJtEdRJEUOAmfj4+Pj4+PQg6lr69/69Ytd3d3hRxNHYwZM2bnzp10p1Ckfv36KeouSTMzswED\nBmhrd3ahlwp0Z442TU1N+a6pNTAw0NHRoX4kTRDETz/91PnpOpXp+KPftGnTsWPHvL29V6xY\nsXz5coU/X0xMzMKFC7lcrpOTk7GxsUgkev78uZub2/nz5xX+XAAA7yL9AC45OXn27NnU+pkz\nZ+bMmUNTKNZS5bJaKmBhYSG9k5o1IiMjFbV0u7Ozs/QaQRazsbGprKzsMNWa+twD2rGx27Vr\n11dffZWYmHj48GEnJ6fW1taTJ08uXbrU3NxcIc9nb29/8+bNrKysvLw82V2xHh4eCjk4AEA3\nSVdnX7VqFfXSGZFItGzZMjR20Nd0fzpY6nVsfZk6T6D7lpOlWlpaM2bMmDFjRkVFxYkTJw4f\nPrxp06apU6fGx8cr6lnd3d3ZdFoeABhn/vz5BEFUV1dLv5Bh2ZkYAAX68ssvx48fT3cK6EJn\nn4LzeLz169evX78+IyPj8OHDKssEAKBsAoGAIAgOh5OTk0O9IREA3iUkJERRhxo/fnyHu4Pf\nSk9PjzpJCkEQGhoaOGvYuW5d3ujt7e3t7a3sKAAAKmZqapqcnDxr1iy6gwC85uLioqgr3tTW\n9OnTu7PbtWvXzMzMqJVly5Z1uVRVH0fzfSsAADQ6cODAnj17HBwcXFxcZFOXKXw2ABazsrKi\nTgwGChEeHk53BHVBncxPatCgQR1m11M2xp0gRGMHAH1XSEiISCTqcP8W+bZp2+Gtjhw5QncE\nAOWaMWOGk5MT3Sl6AI0dAPRd2dnZHSoikYiWJCA3Pp+v1LvxGHfCBhSLcbd7orEDgL7LwsIi\nJyentrZW+rCxsXHhwoXSBZ2AKd5///3ExETlHX/dunWKmrxXTURERChq9mlQQ2js4LXr169f\nuXIlKiqK7iAAKrJ169bo6Gg9PT0dHR0DA4OSkhIFLt4A7MC+ewc//fRTuiOAEml2vQv0Gffv\n309ISKA7BYDqxMbGJicnX79+ffbs2cXFxd99912H5dIBAJgFjR0A9F21tbWenp4eHh5Pnz4l\nCCIsLOzQoUN0hwIAkB8aOwDou5ydnU+dOiW9Or6goEAoFJaVldEdCn6jpaX15lLrANA5xlxj\nV1ZW9vPPP79Zb25uZv1EjgCgJDt27AgODvbz8wsODvb29tbV1fX396c7FPxGW1u7oKAAH44D\n9AhjGruTJ09+/fXXb9aFQmGH9UYAALopICCgqqpKV1c3LCzMycmpsrIyODiY7lDwGro6gJ5i\nTGO3cePGjRs3vlm3trbmcrmqzwMALPDq1SsulytdamLatGl0xwEA6C1cYwcAfVFmZqaDg4Ol\npSWPx0tKSqI7DvQJpqamHVY+BVA4NHYA0Bd9+umnI0eOfPDgwaJFi0JCQrCMGKiAr69vQUEB\n3SmA5RjzUey7aUokRjU1rx+bmr7+ur2dEAoJsdiwqUlPus+bW6n61Naqqipzc03T/+/R3k40\nNelRf5hqmBlbWbmVJDmEyt2/fz8lJcXT03PLli379u379ddfsZg9qICmJs6ngJKRDNe//48E\nQVL/27nz9dY1a0hs7WSrj88FNUyFrX1w6+bNKaRqEQRRUVEh/drY2LigoECxxw99N/kOOHDg\nQHd3d8WG7OPi4uJ4PB7dKUgOhxMfH9/5PpcvX9bV1VVNHqm0tDSCIMRicee7rV+/PiAgoMuj\n8fn8o0ePdr5PRkYGQRAikagHKXsiMjJywoQJXe42fPjwvXv3KimDjY3N8ePHlXRwGQ2S4R9A\nWFm5GRm5nzx5UlZxcSE4///7v7qaEAiIlStXjh49esWKFW/dSqWyrZmZwilTpsTHxw8YMICu\nVBEREdbW9YcO7ZFt/fLLfyYmJp44cULFPw1s7eNbp0+fFh29+KOPFhEqpKGhUVlZaW5uThCE\nqalpZmamnZ2dAo//448/hoeHW1hYTJgwocOm77//Xo4DWltb83i8zMxMRaQDgiCI//znP2vW\nrCkvL6c3hqGh4alTp2bMmNHJPklJSQEBAc3NzSpLlZ6ePm7cOLFYLL216F02bNiQn59//vz5\nzo9mZ2cXFRW1dOnSTva5d++et7e3SCTiyAYIhdq+fXtaWtrVq1c7323EiBErV64MCwtTRgZb\nW9udO3cuXrxYGQeXYfxHsZqatfr6T9577+1bzcwIMzOCw8kdOJD/5j7Sre+i1K0uLvUSyV1H\nR6GT0wC6UpmZCXR0jKhbbWxeGRg8fesPk8afFbayfquOTraWFg1/YcbGxkr/CWlpaTl69Ki0\nySMIYs2aNb0/eEhIiEAgqKiokK+NA2CTqVOnDh06lO4UfQXjGztQvbq6OiMjo673A1BjXl5e\np0+fln7t5uYWHx8v26SQxo4giMDAwPv37yvkUMBi2tra2tpq928xl8vl8/mKuiLw4MGDXe5j\nYWHh6emJhUZ6T+1+mUDNicViS0vLu3fvDhs2jO4sAPKTXtCjVB4eHh4eHsp+FmC69PT0IUOG\n0J2io6FDhxYWFqryGW1tbR88eKDKZ2Qr3J6j1h49epSfn093it8Ri8VNTU319fV0B+lCY2Pj\ntm3bJBIJ3UEAQE1paWl1fgGZagwbNkwNz9gBc6Gx+41YLBZ0uMZbDWzfvv2HH36gOwUjFRQU\nREVFVVVV9f5Qubm5GzZs6P1xALKysrZu3Up3CvjNtGnTfvrpJ7pTMFu/fv369etHdwr4HTR2\nv7lw4cKHH35Id4qOpLcu052ir3v06JHsTmGA3igqKpJd2PcuEomk5m0wFCicvr6+t7c33SmY\nLSIiYv/+/XSngN+h4fRvZWXl8ePHBQJBeXm5ubm560j+SwAAFPBJREFUs7PzokWLaF/vtbW1\nta2tjd4M3fHkyZPc3NzZs2fTHQQAemzmzJkzZ87sfJ8vvvgiKirqrZswty2oG0NDQ0NDQ7pT\ndJeGhgbdEVRB1Y1dSkpKYGCgu7u7p6eno6OjUCg8e/bsli1bEhISxo4dq+IwSlJTUyMUCu3t\n7ZVx8PPnzyckJKCxA1B/8v0Ru3nz5oCAgDfrf/7zn11cXJSTFID9Fi1aNH78eLpTqIKqG7uN\nGzf+8MMPH330EbV49uzZdevWqdu8ALW1tUFBQRcuXOjfv3+PvvHvf/97RkZGQkKCMlJ15+MY\niUQSGhq6c+dOExMTZWQAgC7J/UesgYHBe2+bTNLc3BwzQQDIzcnJycnJie4UqqDqxk4gEPj7\n+3co+vv7S5eFUCuVlZWpqak1NTU9bewkEolYLFZSqu6oq6uLiYlZvXq1WjV2ly5diomJoc4W\nBsBiDPojFgDYRNVXbPj6+m7fvp06WUZjY+P27dtHjRql4iSgYsXFxXl5eXSn6Gjbtm1dLoYD\nIId3/RGrhnffA4CMhoYG0y/FU3VjFxMT8/DhQy6XO3z48A8++MDd3Z3L5aamph46dEjFSYB2\nQqFw8+bN9N7rd+PGDSy+CcqAP2IBmOhvf/tbYGAg3Sl6RdUfxdrb29+8eTMrKysvL092QTEm\nZ++b8vLyoqOjIyIiGHRTlQo0Njb6+PikpKQMGNBxHWFgkJiYmIULF3K5XCcnJ2NjY5FI9Pz5\nczc3N5whBlBnfn5+dEfoLXpmu3Z3d3d3d6flqXtp//79gYGBlpaWssq1a9csLS37+PLGpaWl\nXC5XV1dXGQe/c+cOn8+3srJSxsHVkEgkevToUVVVFRo7RsMfsQBAC7VYxiQrK+v06dPvmrpJ\n6vTp0//4xz/erJeXl9fU1HTeYj9+/LisrCwtLU1WqaysbGlpsba2llVevXpVXV1NPU5jYyNB\nEAsXLqT2K9evXz948CCPx5NVHj58aGRkNHjwYFnlxYsXQqGQeqimpqbi4mJnZ2dZpaWlhSCI\njz/+2MDAQFbMy8uzsrKi3quRlZX14MGD7OxsWUUgEFRVVVEP3tzcXFhYSJ0HQToh36pVq6hn\nwvLz83k8HrWSnZ2tpaVFPVRRUdHLly+pldbW1hcvXlDb1vb2doIg1q5da2xsLCvevXvX2tq6\nw8+TJElqB1xaWlpcXEw9eF1dHUEQAQEB1FV9fvnlFwcHB+rPPCMjY8CAAXZ2drJKRUVFW1vb\nwIEDZZX6+vpXr15R34WGhgaCIObOnUudFT03N5fP5+vr68sqmZmZhYWFP//8s6xSVVXV1NRk\nY2Mjq5SXl3d4QyUSSW5urouLCzX58+fPra2tqW9oSUmJvr6+ubm5rFJdXd3Q0GBrayurNDU1\nFRUVUd++1tZWgiCWL19O/U148eKFhYUFh8ORVcrKynR0dKi/irW1tUKhkPqDamlpEQgE1GUo\nSZJ8+vSpk5OTjo6OrJifn8/lco2MjGSVX3/9VUNDw8LCQlYRCoXV1dUODg7UnB1+NwiCePr0\n6eDBg6k/84KCAlNTU+pvy5sqKytLS0s72YG5ZH/Ezpw5E3cOAYAKqEVjJ52NvfPGbuDAgW+d\nAiAzM5PD4bx1k4yRkZGpqSl1+qicnJy6ujrqd9XX19va2g4fPlxWkUgkenp6Xl5e1OsotbW1\nnZycqP94m5iYGBoaUk+u2NraikQiapPx/Pnze/fuLViwQFYhSVJHR2fkyJHUzuDZs2f29vZ8\nPl9WMTMz09PTo56ssrOzq66upvaIAoHg1q1bCxcupL5kLS0tT09P6vqD9+/fd3Z2pp4o5fF4\nWlpa1G7MwcGhvLyc2geUlJSkpaUtWrSI+kPQ0NAYMWIE9R9vAwMDS0tLU1NTWSUxMbG9vZ36\nE3Z0dCwtLXV1dZVV2traDA0Nvby8qMlTU1M/+OADanfC4XC4XC61PUpJSWlubqYePDs7+8mT\nJ/PmzZNVJBKJvr5+h7cvPT3dx8eH2p0YGxsbGxtT26P//ve/HX43GhoarK2tR4wYIasIhcJr\n16798Y9/pPYrN2/e9PDwoP70BAKBsbEx9VA3btyorKykVl68eJGRkUF9+0iS1NbW7vC7cffu\nXVdX12HDhskqxcXF+vr61EPdvn27rKyMWiksLLxx48aiRYtkldbW1tTUVD8/P2rP/fDhQ0dH\nR09PT1nl4sWLmpqa1EPdv3+/oKCAWiktLU1LS1uwYIEsZ3t7+5UrVz788ENqW/z48WM+n9/5\n/6F37tyh/j/FSjdu3KA7AgD0DSTDBQYGrl27lu4UXTh37pyJiYmSDp6UlNSvX78ud3N1dT12\n7FhPDy49zSkWi3v6jbt3746Oju7pd5EkqampmZqa2vk+oaGhQUFB1MqRI0fs7Oy6PHh2dnZb\nW1vn+4SHh/v7+3e+j/TGRoFAQC2uXbv2yZMn1Iq/v394eDi1cubMmS1btlAr8fHxHA6ny+R8\nPv/o0aPUypw5c8LCwqiVXbt2jR49mlopKCiYP38+tSI9S3rv3j1qcciQIQcOHKBWlixZsnz5\ncmplz549I0aMoFZu3rxJEERzc7OsIj1VnJ6eTt3N09Nz9+7dnb86Gxub48ePd74P0/V+BGDE\nWAdKcvnyZV1dXbpTQG+pZqzDkmKqoKmpSftaQElJSdRP1pRt/fr1Knuu7nNzc+tynyFDhsj3\nZu3Zs6fLfQIDA1V5v5Wdnd2pU6e63E1XV1dJ10eCzN69e+mOAAB9gqq7jZSUFAcHhzNnzpAk\n6ejoqKmpefbsWQcHh/T0dBUnUaVJkybFxcUp6eBmZmbUTxLfxcbGhnpZFaPZ2tpSP7BWrJCQ\nkJ07dyrp4OopMTFx8eLFdKdguSVLltAdAQD6BCwppgr9+/efNGmSkg7u5eVVUlKipIOrXnfO\nboaHh6smTB+hqDuOtbW1w8PDqVcZAgCAimFJMVAvFy9e9PHxoTsFA0yaNIl6QwlBEN7e3tK7\nrVXDyspq9OjRHU4DR0dHqywAAAC8SdWNnXQ29ujoaNnEDY2NjTt27MBs7CA1depUuiN0TXof\nKPWuVdX75JNPOlQmTpw4ceJEhRy8X79+1Lue38re3v727dsKeTrojl9/fe/Zsw9XrXpdWbqU\neP/9376+dIn46aff7Y+tbNp69y5PLN6Hd5/pW2trv6qq6tnq83JQdWOH2diZxdXVNSIigt4O\nRg3Z2Nhcu3aNOqmHsnWn0+oOQ0PDPXv2dDmf9l//+ldFrZbo4eHh6OiokEP1ca2t/VtaDGpq\nXleEwtdf19QQ1E3YyrKt9fU6JGmCd5/pW9vbTVtalL6KpgZJx0qdCpyNfc6cOTY2Nt25IRFY\n7NixY5GRkeq2vPr06dOHDRvW+aeTFy9eXLBggUgk6vxQRUVFVlZWNN7+snfv3kOHDmVlZSnj\n4La2tjt37sQNHJ3DWNeXJSUlBQQENDc30x0EekU1Yx2WFAM28Pf3786twcylvLuAu8nOzg53\nRQAAqD+1WHkCoJe4XO60adPoTiEPbW1t6gIhaisgICAgIIDuFAAA0AUG/IsCwFBLliyhLmj7\nVpMnT2b3JI4AAKBKaOwAlGX+/Pld7qOtrU1dARYAAKA3aF7nCgAAAAAUBY0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      "text/plain": [
       "Plot with title “PACF of squared returns of Y1”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create Autocorrelation and partial autocorrelation plots\n",
    "par(mfrow=c(3, 2)) # set up the graphics  \n",
    "acf(j1, 48, main=\"ACF of Y1\") # autocorrelation function plot \n",
    "pacf(j1, 48, main=\"PACF of Y1\") # partial autocorrelation function \n",
    "acf(ts(j1, freq=1), 48, main=\"ACF of returns of Y1\")        # autocorrelation function plot \n",
    "pacf(ts(j1, freq=1), 48, main=\"PACF of returns of Y1\") \n",
    "acf(ts(j1^2, freq=1), 48, main=\"ACF of squared returns of Y1\")        # autocorrelation function plot \n",
    "pacf(ts(j1^2, freq=1), 48, main=\"PACF of squared returns of Y1\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusions\n",
    "\n",
    "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) **5% level of significance**.\n",
    "\n",
    "So we conclude  that:\n",
    "\n",
    "* From **ACF plot** of the residuals we observe that we have **autocorrelation for lag=1**. We must check a **moving average** model for lag=1. **(MA(1))**\n",
    "* From **PACF plot** ofr the residuals we observe that we also have **partial autocorrelation for lag=1 and lag=15**. We must check a **restricted autoregressive** model for lag=1 and lag=15. **(AR(15) restr)**\n",
    "* From the upper (time series) plot of the return series we observe that the volatility of the return series **is not constant** over time. There is evidence of **volatility clustering phenomenon**, since there are periods of high and low volatility. "
   ]
  },
  {
   "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 Y1**\n",
    "* **create the plot of the histogram together with a density plot**\n",
    "* **also create the normal QQplot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  j1\n",
       "W = 0.96158, p-value = 0.000138\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mGlSabhblcTniFFxjvdHThZp6mYcZH71QQjhMTZFkOlPV2fnhRjGftUld1fLT3d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DHK6Wg6pN6NygIRUkD+Nb0URiGV7JUcUc4+Gk09D6p9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\nAYgEgAZ+A8kXJ3/DXFKUAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Normal QQplot of Y1”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Shapiro test of normality\n",
    "shapiro.test(j1)\n",
    "\n",
    "par(mfrow=c(2,1))\n",
    "hist(j1, prob=TRUE, 20) # histogram\n",
    "\n",
    "lines(density(j1))\n",
    "# smooth it - ?density for details\n",
    "qqnorm(j1, main=\"Normal QQplot of Y1\") # normal Q-Q plot\n",
    "qqline(j1) # add a line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusions:\n",
    "* From Shapiro Wilk test (p-value = 0.000138) we **reject** the Null hypothesis for Normality.'\n",
    "* From the Histogram we see a left skewness.\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 -  UNIT ROOT TESTING"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autoregressive Models (AR(p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we can fit an **autoregressive time series model** to the Y1 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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "ar(x = j1)\n",
       "\n",
       "Coefficients:\n",
       "     1  \n",
       "0.2481  \n",
       "\n",
       "Order selected 1  sigma^2 estimated as  0.0003725"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "'Order: 1'"
      ],
      "text/latex": [
       "'Order: 1'"
      ],
      "text/markdown": [
       "'Order: 1'"
      ],
      "text/plain": [
       "[1] \"Order: 1\""
      ]
     },
     "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",
    "m1 = ar(j1)\n",
    "m1\n",
    "paste('Order:', m1$order)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking autoregressive model without drift and without trend"
   ]
  },
  {
   "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: -8.7817 \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)\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.086629 -0.006201  0.007275  0.018381  0.056157 \n",
       "\n",
       "Coefficients:\n",
       "        Estimate Std. Error t value Pr(>|t|)    \n",
       "z.lag.1 -0.63308    0.07209  -8.782 1.91e-15 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.02017 on 166 degrees of freedom\n",
       "Multiple R-squared:  0.3172,\tAdjusted R-squared:  0.3131 \n",
       "F-statistic: 77.12 on 1 and 166 DF,  p-value: 1.911e-15\n",
       "\n",
       "\n",
       "Value of test-statistic is: -8.7817 \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": [
    "m11 <- ur.df(j1, type='none', lags=m1$order-1)\n",
    "m11\n",
    "summary(m11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The Critical Value (CV) for 5% is -1.95\n",
    "* The value of the test statistic for lag=1 without drift and without trend is: -8.7817\n",
    "* z.lag.1 is statistically significant\n",
    "\n",
    "Obviously, the null hypothesis of non-stationarity for the Y1 series is rejected. Therefore the returns of Y1 seem to be a stationary process.\n",
    "\n",
    "### Checking autoregressive model with drift (intercept) and without trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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: -9.9769 49.7692 \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)\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.094517 -0.011083  0.001633  0.012123  0.054239 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  0.006449   0.001631   3.953 0.000114 ***\n",
       "z.lag.1     -0.751732   0.075348  -9.977  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.01934 on 165 degrees of freedom\n",
       "Multiple R-squared:  0.3763,\tAdjusted R-squared:  0.3725 \n",
       "F-statistic: 99.54 on 1 and 165 DF,  p-value: < 2.2e-16\n",
       "\n",
       "\n",
       "Value of test-statistic is: -9.9769 49.7692 \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",
    "m12 <- ur.df(j1, type=\"drift\", lags=m1$order-1)\n",
    "m12\n",
    "summary(m12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The Critical Value (CV) for 5% is -2.88\n",
    "* The value of the test statistic for lag=1 with drift is: -9.9769\n",
    "* Both Intercept and z.lag.1 are statistically significant\n",
    "\n",
    "Obviously, the null hypothesis of non-stationarity for the Y1 series is rejected. Therefore the returns of Y1 seem to be a stationary process.\n",
    "\n",
    "### Checking autoregressive model with Drift (intercept) and Trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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: -10.1882 34.6052 51.9076 \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)\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.094640 -0.012259  0.001255  0.011391  0.056413 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  1.126e-02  3.198e-03   3.520 0.000558 ***\n",
       "z.lag.1     -7.761e-01  7.618e-02 -10.188  < 2e-16 ***\n",
       "tt          -5.475e-05  3.138e-05  -1.745 0.082899 .  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.01922 on 164 degrees of freedom\n",
       "Multiple R-squared:  0.3876,\tAdjusted R-squared:  0.3802 \n",
       "F-statistic: 51.91 on 2 and 164 DF,  p-value: < 2.2e-16\n",
       "\n",
       "\n",
       "Value of test-statistic is: -10.1882 34.6052 51.9076 \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": [
    "m13 <- ur.df(j1, type=\"trend\", lags=m1$order-1)\n",
    "m13\n",
    "summary(m13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The Critical Value (CV) for 5% is -3.43\n",
    "* The value of the test statistic for lag=1 with drift is: -10.1882\n",
    "* Both Intercept and z.lag.1 are statistically significant\n",
    "* Trend is **not** significant.\n",
    "\n",
    "Obviously, the null hypothesis of non-stationarity for the Y1 series is rejected. Therefore the returns of Y1 seem to be a stationary process.\n",
    "\n",
    "**Thus the model does not have a trend!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now we will check the autoregressive of lag=1 model (AR(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "arima(x = j1, order = c(1, 0, 0))\n",
       "\n",
       "Coefficients:\n",
       "         ar1  intercept\n",
       "      0.2473     0.0087\n",
       "s.e.  0.0746     0.0020\n",
       "\n",
       "sigma^2 estimated as 0.000368:  log likelihood = 425.8,  aic = -845.61"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar1fit <- arima(j1, order=c(1,0,0))\n",
    "ar1fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The estimated model (AR(1) can be written in the form:\n",
    "\n",
    "$$y_{t} = μ*(1-φ_{1}) + φ_{1} * y_{t-1} + e_{t}$$\n",
    "\n",
    "$$or$$ \n",
    "\n",
    "$$y_{t} = 0.0087*(1- 0.2473) + 0.2473 * y_{t-1} + e_{t}$$\n",
    "\n",
    "$$or$$ \n",
    "\n",
    "$$y_{t} = 0.00654849 + 0.2473 * y_{t-1} + e_{t}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moving Average Models MA(q)\n",
    "\n",
    "#### We check the moving average of lag=1 model (MA(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "arima(x = j1, order = c(0, 0, 1))\n",
       "\n",
       "Coefficients:\n",
       "         ma1  intercept\n",
       "      0.2223     0.0087\n",
       "s.e.  0.0687     0.0018\n",
       "\n",
       "sigma^2 estimated as 0.0003704:  log likelihood = 425.27,  aic = -844.54"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ma1fit=arima(j1, 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",
    "$$y_{t} - 0.0087 = 0.2223* e_{t-1} + e_{t}$$\n",
    "\n",
    "$$or$$ \n",
    "\n",
    "$$y_{t} = 0.0087 + 0.2223* e_{t-1} + e_{t}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lets now fit an ARMA(1,1) model. The command is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "arima(x = j1, order = c(1, 0, 1))\n",
       "\n",
       "Coefficients:\n",
       "         ar1      ma1  intercept\n",
       "      0.2931  -0.0484     0.0087\n",
       "s.e.  0.2557   0.2637     0.0020\n",
       "\n",
       "sigma^2 estimated as 0.0003679:  log likelihood = 425.82,  aic = -843.64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "arma11fit <- arima(j1, order=c(1,0,1))\n",
    "arma11fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The estimated ARMA(1, 1) model can be written in the form:\n",
    "\n",
    "\n",
    "$$y_{t} - μ = φ_{1}*(y_{t-1} -μ) + θ_{1} * e_{t-1} + e_{t}$$\n",
    "\n",
    "$$or$$ \n",
    "\n",
    "$$y_{t} =μ +  φ_{1}*(y_{t-1} -μ) + θ_{1} * e_{t-1} + e_{t}$$\n",
    "\n",
    "$$or$$ \n",
    "\n",
    "$$y_{t} = 0.0087 +  0.2931*(y_{t-1} -0.0087) - 0.0484 * e_{t-1} + e_{t}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summarizing we have the following:\n",
    "* AR(1): \n",
    "  * Variance: **0.000368**\n",
    "  * AIC: **-845.61**\n",
    "* MA(1):\n",
    "  * Variance: **0.0003704**\n",
    "  * AIC: **-844.54**\n",
    "* ARMA(1, 1)\n",
    "  * Variance: **0.0003679**\n",
    "  * AIC: **-843.64**\n",
    "\n",
    "  \n",
    "### Conclusion:\n",
    "\n",
    "* The model with the lowest variance and lower AIC score is the best. \n",
    "* Here, **AR(1)** has both the smallest variance and smallest AIC. Thus, it's the model that best fits the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diagnostic plots\n",
    "\n",
    "Now we will provide some **diagnostic plots** for the **residuals** of the best model (AR(1)).\n",
    "Based on the residuals of the restricted AR(1) 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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Tvl5uZ279798ePH5ubmXMfSDA4Ku8TE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7pNi8efNknARA2o4dO9akr+LxeK3fH/oh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",
      "text/plain": [
       "Plot with title “Normal QQplot of residuals”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar1residualsTS <- ts(ar1fit$residuals, frequency=12, start = c(1991, 1), end = c(2004, 12))\n",
    "\n",
    "par(mfrow=c(3,2))\n",
    "\n",
    "# set up the graphics\n",
    "acf(ts(ar1residualsTS,freq=1), 48, main=\"ACF of residuals\")\n",
    "pacf(ts(ar1residualsTS,freq=1), 48, main=\"PACF of residuals\")\n",
    "acf(ts(ar1residualsTS^2,freq=1), 48, main=\"ACF of squared residuals\")\n",
    "pacf(ts(ar1residualsTS^2,freq=1), 48, main=\"PACF of squared residuals\")\n",
    "qqnorm(ar1residualsTS,main=\"Normal QQplot of residuals\")\n",
    "qqline(ar1residualsTS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the residual plots presented above:\n",
    "\n",
    "* From the ACF and PACF of the residuals, it seems that the assumptions with respect to them are satisfied\n",
    "* From the PACF fo the squared residuals it seems that there is an **heteroskedastisity** issue \n",
    "* From the Normal  QQPlot of residuals only 3-4 points are of the line. So we assume normality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecast and Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kdqhfxCTZ7ILdiJrVjVBYqLN0r4TLZnz56BgYH169dzsMPpC7JCsCuPoaEhu93e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RG2+8UZ2w1VrgZp3L5QKBACtiYqFYk8Iu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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forecast <- predict(ar1fit, 12)\n",
    "\n",
    "# plot of forecasts with 1 standard error\n",
    "par(mfrow=c(1,1))\n",
    "UL <- forecast$pred + forecast$se\n",
    "LL <- forecast$pred - forecast$se\n",
    "\n",
    "predTS <- ts(forecast$pred, frequency=12, start = c(2004, 12))\n",
    "UL_TS <- ts(forecast$pred, frequency=12, start = c(2004, 12))\n",
    "LL_TS <- ts(forecast$pred, frequency=12, start = c(2004, 12))\n",
    "\n",
    "min_x <- min(ar1residualsTS, LL)\n",
    "max_x <- max(ar1residualsTS, UL)\n",
    "\n",
    "ts.plot(ar1residualsTS, predTS)\n",
    "lines(predTS, col=\"red\", type=\"o\")\n",
    "lines(UL_TS, col=\"blue\", lty=\"dashed\")\n",
    "lines(LL_TS, col=\"blue\", lty=\"dashed\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Squared Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.000118806097790841"
      ],
      "text/latex": [
       "0.000118806097790841"
      ],
      "text/markdown": [
       "0.000118806097790841"
      ],
      "text/plain": [
       "[1] 0.0001188061"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(hydroGOF)\n",
    "MSE <- mse(forecast$pred, forecast$se)\n",
    "MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$MSE = 1.188* 10^{-4}$$"
   ]
  }
 ],
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