Lista Prática 4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lista Prática 4 - Pablo Corrêa Fonseca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Importe para o R os dados do arquivo “dados_03.csv” e converta as variáveis YIG,\n",
    "YIGD, IBCBR, IBCBRD, IPCA e TJ para séries de tempo usando o comando “ts”. [Obs.:\n",
    "YIG = produção física industrial; YIGD = produção física industrial dessazonalizada; IPCA\n",
    "= índice do IPCA; TJ = taxa Selic; IBCBR = índice de atividade do BCB].**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "               TJ    IPCA  IBCBR IBCBRD  YIG YIGD\n",
       "2003-01-01 1.9713 2085.68  96.15 100.44 74.0 79.3\n",
       "2003-02-01 1.8304 2118.43  98.67 101.83 71.8 79.5\n",
       "2003-03-01 1.7770 2144.49 103.41 102.17 77.4 79.5\n",
       "2003-04-01 1.8716 2165.29 102.19 101.43 76.5 79.2\n",
       "2003-05-01 1.9654 2178.50 100.30  99.67 79.7 77.9\n",
       "2003-06-01 1.8567 2175.23  98.58 100.39 76.3 78.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library('xts')\n",
    "df = read.csv2('dados03.csv', sep=\";\", dec=\",\")\n",
    "datas = seq(as.Date(\"2003-01-01\"),length=nrow(df),by=\"months\")\n",
    "df = xts(df[0:-1], datas)\n",
    "head(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2 . Crie a variável “taxa de juros mensal real (ex-post)”, por meio do comando:\n",
    "“tjr=((1+tj/100)/(ipca/lag(ipca,-1))-1)*100”. Realize o teste ADF para esta variável, nas\n",
    "especificações com constante e com constante+tendência. O PGD possui raiz unitária?\n",
    "Parece estacionário ou não estacionário?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "               TJ    IPCA  IBCBR IBCBRD  YIG YIGD      TJR\n",
       "2003-01-01 1.9713 2085.68  96.15 100.44 74.0 79.3 3.572485\n",
       "2003-02-01 1.8304 2118.43  98.67 101.83 71.8 79.5 3.083073\n",
       "2003-03-01 1.7770 2144.49 103.41 102.17 77.4 79.5 2.764163\n",
       "2003-04-01 1.8716 2165.29 102.19 101.43 76.5 79.2 2.493098\n",
       "2003-05-01 1.9654 2178.50 100.30  99.67 79.7 77.9 1.812347\n",
       "2003-06-01 1.8567 2175.23  98.58 100.39 76.3 78.0 2.060392"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "'drift'"
      ],
      "text/latex": [
       "'drift'"
      ],
      "text/markdown": [
       "'drift'"
      ],
      "text/plain": [
       "[1] \"drift\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>tau2</th><th scope=col>phi1</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>statistic</th><td>-4.855875</td><td>12.10422 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & tau2 & phi1\\\\\n",
       "\\hline\n",
       "\tstatistic & -4.855875 & 12.10422 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | tau2 | phi1 | \n",
       "|---|\n",
       "| statistic | -4.855875 | 12.10422  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "          tau2      phi1    \n",
       "statistic -4.855875 12.10422"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>1pct</th><th scope=col>5pct</th><th scope=col>10pct</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>tau2</th><td>-3.46</td><td>-2.88</td><td>-2.57</td></tr>\n",
       "\t<tr><th scope=row>phi1</th><td> 6.52</td><td> 4.63</td><td> 3.81</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & 1pct & 5pct & 10pct\\\\\n",
       "\\hline\n",
       "\ttau2 & -3.46 & -2.88 & -2.57\\\\\n",
       "\tphi1 &  6.52 &  4.63 &  3.81\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 1pct | 5pct | 10pct | \n",
       "|---|---|\n",
       "| tau2 | -3.46 | -2.88 | -2.57 | \n",
       "| phi1 |  6.52 |  4.63 |  3.81 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     1pct  5pct  10pct\n",
       "tau2 -3.46 -2.88 -2.57\n",
       "phi1  6.52  4.63  3.81"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "'trend'"
      ],
      "text/latex": [
       "'trend'"
      ],
      "text/markdown": [
       "'trend'"
      ],
      "text/plain": [
       "[1] \"trend\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>tau3</th><th scope=col>phi2</th><th scope=col>phi3</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>statistic</th><td>-4.98501</td><td>8.672161</td><td>12.69247</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & tau3 & phi2 & phi3\\\\\n",
       "\\hline\n",
       "\tstatistic & -4.98501 & 8.672161 & 12.69247\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | tau3 | phi2 | phi3 | \n",
       "|---|\n",
       "| statistic | -4.98501 | 8.672161 | 12.69247 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "          tau3     phi2     phi3    \n",
       "statistic -4.98501 8.672161 12.69247"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>1pct</th><th scope=col>5pct</th><th scope=col>10pct</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>tau3</th><td>-3.99</td><td>-3.43</td><td>-3.13</td></tr>\n",
       "\t<tr><th scope=row>phi2</th><td> 6.22</td><td> 4.75</td><td> 4.07</td></tr>\n",
       "\t<tr><th scope=row>phi3</th><td> 8.43</td><td> 6.49</td><td> 5.47</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & 1pct & 5pct & 10pct\\\\\n",
       "\\hline\n",
       "\ttau3 & -3.99 & -3.43 & -3.13\\\\\n",
       "\tphi2 &  6.22 &  4.75 &  4.07\\\\\n",
       "\tphi3 &  8.43 &  6.49 &  5.47\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 1pct | 5pct | 10pct | \n",
       "|---|---|---|\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",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     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"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df$TJR=((1+df$TJ/100)/(df$IPCA/lag(df$IPCA,-1))-1)*100\n",
    "head(df)\n",
    "library('urca')\n",
    "t1 = ur.df(y=na.omit(df$TJR), type='drift', selectlags='BIC')\n",
    "t1@model\n",
    "t1@teststat\n",
    "t1@cval\n",
    "\n",
    "t2 = ur.df(y=na.omit(df$TJR), type='trend', selectlags='BIC')\n",
    "t2@model\n",
    "t2@teststat\n",
    "t2@cval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "tanto no teste drift, quanto no trend, rejeitamos a hipótese nula de que há raízes unitárias, e o PGD de TJR parece ser estacionário em torno de uma tendência"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3 . Estime a regressão de tjr em uma constante e uma tendência linear. Apresente um\n",
    "gráfico com a série original e a ajustada, e outro gráfico com o resíduo da regressão.\n",
    "Qual poderia ser a interpretação econômica da variável ajustada da regressão? E do\n",
    "resíduo?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = coredata(df$TJR) ~ seq_along(df$TJR))\n",
       "\n",
       "Coefficients:\n",
       "      (Intercept)  seq_along(df$TJR)  \n",
       "         1.823226          -0.003501  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r1 = lm(formula = coredata(df$TJR) ~ seq_along(df$TJR))\n",
    "r1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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OCFzyM9amdVzcPjXovjV9IgcXK2Mum7\ntYFBah4t0vxThDyL0KxwoGmnlVmu6oLUmuZ82fdPY75VNXovQrXKjxh1g+0o8VqE5KcgoYMN\n9weaSG+QTfEBjFzkwLDCMiTfkMETsv/OzzPZSb+vL0WQRtp++lKLkfjUIuGVDUUVMRwkpl7h\nablB8rnshyDBU3CQfnbnHXZ3FNVnqAivNcydIw+exBEkeJIMNvz9WyNNkiBIc+sZuRBcVDzW\nJjBIe7M9nffGvdU39nkV4b6wMVZNy9C5H6N28BM8IXuKsfMFrOy1Nu4rYh4JPgSXCBUWpJcV\nEAqkERikza1FOlh8rYtnEX5L0tlBUpo+0k9zvo1cRxAkOjtIKXTUbne7REj6fEhJixSrs0Mn\nqnZRtqBkHsns/omqM1iEx6KKiajBddDS1S7SFlzclQ3en9NLckbXQt+rdpG2YGCQdhY3xnoI\nnkfyWKjrJ2fs02Y0sHaxtqBg+DuC9Pvp8Kj5Rz0IUu0KDdLzyUBSyffTt4+XIC1WoUE67baO\nX4zkXMTUy2QNom2Q6CNVr8w+UvB3g80XMf4i4fDL8Dnd0GADo3aVK3PULmuQ7F/qvLKJT5t5\npNqVOY8UxWgR0R5D+5Ec8gIXlQXp2QbKe40kBwGCg/Rvm+fKhsd+z+6PAoQG6f44rgzX2kXp\nnaFeWXeFwCDtzeUh+lmu/p75ziOsi91oXLR9JXhC9v7I4hz3Iz0/FRqn1bMZxI04eaG6RKiQ\nO2TJ0lpZjT1FnE6XtUjFPESfxmmVbIIU8wKvivtIc+sgSytxfSDc/ZepF1q8xrsSgYtkHLWz\nWM1lvolALdq932Nx2lZykG4P0S/nDtn3NelO9Ehkke4BshlIKLePFIkwSLc/g8O0+KtVKz1O\n9FqZ+XdQ7qhdJLIiXhrzoMYp4sGsBNUeJxxP10qdR+pO7Xm4rmm19/fFCdL9Z58PM+bpdQmq\nPU6UsmECg3Rsboey0h6i/7ai9xU6N06lbK9IKn57hRwCAoO0NV/ntujUar/7Ut9HGvm/1mGq\neE+zUfHbK+SkdGFXNnyuafZjtmycCjnwRVJWkBzPvYsYJgkMUnN7+Mmp1CBZf8xzYSrkwBdL\nQceJOj/pwCC15vLwk9+tkT7gLtOnON04FXHgi6WgvbegTDtY9JUNvqUvOjJjSnnTZZ1lWtNc\n2bCVXmkn/xAH9pG53Sbrla+59+ki7pBzq0Luj2zpE7KXlX2etVifyOQIU+6zrMzl+wSpgHs8\n1xCkz1XanYbftkrqMOXuI1RY/m0Rt0OAdrMuP0gDRzirg97LVkl4ppe7j5C7fI8W8bXKdkuq\n212CNL3c60tSZCn3jpy7/M79Y34c7V5+tVmGILmvyzFIY6+JfgNuzh05xvMCE/AIkvxdLj9I\nnn2kuU86Xpay9VFuZzu5+0geXqtMkOIU4TdqZ/FJR2qcso2aeXXZi+B+CCBIXqtzn0dyaRjk\nWcoziPvct7JPyri7PrfhcQhQbl7LCiRZpMAiZjkdmJfw6KIKO0cfTD9LM6+cf41TyUkWKbAI\nCx7BqDFL76dEmd6B8KOza22YRypbZY1T78h8/SNPzZUNRJYjAkHyNLvDVZKl3tHbmPsDzLJW\nQ7QughS9CMEubncAraBxet3pTK9pyliN+ZdP36rptjKN9QVJchLhdgD1etpKjguSsnWTnAqe\n3YI5ZsJWGCRBCe47nGPDlGwup8ogzb00x0zY6oIk2Vf8VuJwopfumPpSUr6BO4c3bFPJ9OfT\nBCn5SizCNLV+8T7yevQe25+j75gOjUjmYfoRBClgLf7rmGmcxit5n7cXfULXQTrT+70b2J+T\nnCpZvyeCVEYRkrMm0a41loiJIHVd73KY4OK7jxUN1ShH531CYdW5WmGQZBkQVKYbaZxGT7Fu\nfxjJZ2S5R5bWBBR5Ve36gpSjJzrJDJyuje0r5u2/sILf/g59XTqFbcGzNQapKP3I9Bun4X2F\nIJWKIPmIe4HlzDDE/bQuWZDK7JQUhiC5S3GB5diw3nWcQdIg2QekyE5JYQiSO+UBeqZVGAiT\n0d3Car+iAjslhSFIzqRdBouVDTRO0nkkKCw7SFH2E23f2655K/8y8rVbcpAindqLg2RRycdr\nyJOY7sNMH6T9xpjdT9QiXtai3+3E63V/UAdh0ogxahR3ketylwVv3wMz/XVKqbofnitOPIg1\n+EaWmqWU7yvGqFHcRa7LnRdszfkL0I+tmfwimLKDlHovNiOFVnADrqukx6goo0ZxF7kud17w\n9l2ZJ7OJUcTgSqrf0a7Tr+eHCY9c4rqcLCWd+q06SMb0fpEXMbSWnDuZaBe/zr9OzcIupHFK\ne+yrOkhf9yA1MYoYKDDjzqWcOL23RjNrqzxLiU8iqu0j7b73P+bf34+ndnq0oeh5JPvSe3+G\nrurRktu8tNrGKXWQah21e2xhY5pTjCKKEuXMwX5lVWYp9dl4nfNIh8N+v9tdhhzayRzVH6TL\nLdz3nzVr9FhXfY1T7rNx/2iln5AtpIiYhh4ool2n67L1fKCZz8a9P2WCFMGt9RCfpwTtYvU1\nTln4bzKCpPdoigLPU2Ls92RpSsBJRK4gpZhHyuW5OUJ2W0V3YbB8GqdRiwiS6VMU4S+wAprO\nUfiJ4UwUs3/M5akwSNmLmCg8uClQdI4EaZyvRv5jVmHoI8kL9/lgXq5/Cj0re/s72hp8zgEW\nmz9G7fRlu9bh7VLC0LeQLEj3V9lXWfxOHUUukHkkddnOQfJaKuL63N+IZePUq1nyCVRVgfI4\nEqSxsh3roJ1+7ax2mZm9wTeKM2Hqv1P10WOWpsAI+SdII4X7NUjSqs/lZG5vCLwYYixPvXca\n4U1PExUYIf8Jg2RexShCwm//c9jEwruUZsq7XPJnUdroa4Y2VP1BilHthEHaVxIkzz3d9ign\nO8t/+9u/tPn5ptft9XynEYP0uQ10FwJXHqTu0GxjF5GRbUBUpxWWQRK9pt849d5prD7S54d5\n+5egAt8XrzVI3WHm4UGCInIyb1t+rocRWJrNimxe5HZSal5OF2ON2n3mxdwr4F1g3PynHWzY\nm0PsIgoxusFHd1vn80n7xkYWpPsre3WNMq3zWaXnv3gX2Pu8GLWrxuhePrLbemxaq+7PcGnO\nrxkqPeJFkVNB0qxzsuo+74sgRTGx3Ycj5nWy4TZ5GvSaiSrMLBiyV8YL0tQLvZorgiQ3M7o0\nuJ1idH/HS/N4zfTy48t6rnu0j+S6ovcV2ATJqySCJPa65wyPN0zOzegrNL9S21Zjcr5psHHy\n3P9HR+1cV+ReFc9NQZDE7qfgvV+slwrqS8fncdGS/wFieB7Jb8n7v3c2USRIRXhsBscDaL8L\nXGqU7A4OL41TxJZ2tPhu9BO0iiJBKsFzgsWpaTH3BAX3BCJy3MMubyZDkILLo4+UnbF+tPD7\nYrcspd/vHLhX7tE4pc5R2KgEo3aZ9JqhS1PUOb6B5yFwYUHqngcJfXVGynv7228lzCNl8DyA\nmduvY1+/MraC599lB8m9rX0uZnOpsoLfJyioGEEK9dGeuG6V/rYvt490vcLO8RgxtJrIb87j\nE5SM8BCkQOHtyUuQih21uzW3gvH5uI2Tz7VWvT/9y02ySIFFqAjak5fFCp1HerxNXdJjvdOQ\nM4KAUpMsUmARKoL2JHjqI4HXvU1VJ8v7POMiSGVQtCeBk/EJPN7fy6+ideeNEkEqQ8ydPerY\ng/W+25tafe50dlcJWBVx737lilNvuMi/fIIULuFtOcJ12+b/OV3ce73V0q4Xt6Wec3pU4FbP\noEMiQSqYMkjDl5PaBOn+Z79hslrasoiXcN4au5GF4o5PBLX/BKlguiB9HGytV/32Qou7RFyL\neH9d/0zv9YVxe4xhnzZBKpmsj/SxIt8gXY/e0iC9tnKvr38JU9QeI0FaMtUx+HMf8Q+S9dL2\nRbz2jd5f/37la6ydgyBVw+NmNc0jEQb2kbnD+8uVuB8vVPaRHoVNv/7jHic5+kil6w15vez2\n4Q2O/12f00v2/u/gC5WjdravN8M9Jx1G7cr2GF29/tb/Px//Mrsqn5Zh5HVTe+TL6wdfKJxH\nsn39o1LRwsQ8UslG+9KuJ+UDTZrtGhwPtrG7I35e3oSucRKtJckiBRaRzPtOGRCkj1c7rMFp\ndykzSCOdzLBKqsdz4i5SYBHJuARpcq8YHTHQf15JgxQ8/RrUOKkGMAhSbI+dcraPNHZwfLs1\nNaiXZSnWegdKGmsRnJsKrzDJDhkEKbr7Tjk7aje89z5eNBgk0YnJu3SXnY9G1ivLzo0TQapH\nf+x74BT/+fPb3y+/mm5k1ypwAMupmLe/3/+HXzXsw0SQauJwN0H3/uZ7/5qumQiiaRGuZ7PO\nT5JxrgZ9pMWZDVKyZiKEaqD93i00AXuDzT1OjNotz/Cp29vfpXM9wk/1kcwzT2F1mp7nZR5p\nYYYPjukG0BSccz81aufz2NrRYiLfgEuQYnPZekOvraRndOPRgM7PIwnffPS7meMuUmARiShi\nUEHP6EF7JhqlNY7TOBGkuOo6MROQvuGorbE2SwQpqtqGCsKJ9/24rXG/cQosiSBF9QxSTedn\nYSp8p+8PSfJZRZJFCixCbGTveQSpqhGDFTKhPSeCpDCeE/P8//W9rSBVNUzhZw4ESWE8J68R\nq+19+ausCX6/fsS9cSJIApM5SfEAnPK8HFrKb5wGN5DXRYMehUZU+uf+ZjYnqwtS/w1XMZU2\nck7hfhm5c5lRVbbDzedkbX2klyC9/IvX2uKfJw4V8RwXt8gTQVKY3Vcq6zIE6wVJ0BonOQy9\nZ+V9k81dRe5RovsiBRYhZZGT8vsJUs99PzxIeU6MHdNLkAL0wrGynMzq3RZ8/xf/dQWvIUGh\nBMlb0Ona8oP3du128JkdQfJQxU4WsIOsqssU/mZzDNUQpFRCjpMrG8Qr5SGOboX2/rR+uUcJ\nUdWwiwUEaXXTSsEynAl7PnzCpQT3RQosIhhBWjqubEjD6/zMjD3qEXUjSN48ztzvi6ysj7QG\nBCmA85n7PUB1jNotf4heiCAl1L9wRriTxtnhmSZzQpASitI3ivYc/d6frotW0eBqEaSE4gRJ\nv8r+Cpkms0OQUoqwh8UaAbxf3+PRsCxiUJI7ZEsW4ZzHZq/1ToPft0EsIEjuG4ogpSW/YHx4\nr3353iW/9F6WerkRIqxKVXE/dSBImcgap4FtPvTEles/uUzV+z/Efmw3rGYsz+NQQJAykXWX\nBhL5su7HTuEcXe+H2A+XVNFY3jNIPLOhcMrTn4+bpF/+fgbJuUD3St6rMvi1Gs7lZ/PymdlF\niSDlEbMfMRIkjxId9/3J/a6qntP9cND7xWoJj0KiquLDDpIuSK87hWOQ3M7GJve7uoI00Muc\nWcKjEPdFCiwit5gnOgPndMYrSHbjA+/nc8NLVBWkzvm5ngQpk5hd7+EnSUWK7uOK9ssNIs+C\nPl8Yp/yICFJC/kO6Ub/RdKizHye693w855zGglTPqN0dfaRU6to5YkS3f9S+/jdexmf5hc8s\nMWqXSr7TlVJ2wZcgGbd6VXAYYh4piWwd6HJ2wbexdo/r00p4F3MKe/b37/fu8jzyXfsbq4i0\n8gUpT7FDnn2k528uSxbyNqbYHLYSBum0MU/bKEWklmtXKGkXfI7adY6NZEnvYpLNMSJhkFrT\n/Dtcfjr+NKaNUURymVqGsnbBqeuCJpd7+7tUVvVMGKTGHB4/H0wTo4jkMvVVbDZtKaMREwo6\nQZ1SWpBeNuz0Vi7+s33Ks7/O7oLljEZMqKKS5QVpiS1SLrO7YC0H+/Jj1JXYR/o5Xn5aTh8p\nn+ldsJbuRx0KG7Xrtr1Ru80pShG4Ikhapc0jtZd5pGb3vZB5pHK8bWmClBpXNizB57lHJX2k\n5SBIS/AZm0oGxJaDIC3A4IlcHQNiFbEb3nFZoXdV+itZyjxSCSrqEVUb77kmvpwgmT5FEetR\nTZAqPuGc63RyarcEL1u54ONQvUMgs8cqgrQEvSN9yQf9alrOTwRpJd6eilreB/j5VJ6CW85P\nBGllkh707aPw+Zy4klvOIfSR1iVhkFyicG+Dnr+U2nKOKXXULnsRC5UySPYFPWr1bIve/k8F\niplHMsZ6hLuij7cg10c0Xn9MUNrb33avfX8a62K2dMIg7QlSTPcnE6fqe/gFyWfpKqQ8tTs0\n0488ERSxYrfBb4ev9BGU11luq892srY+0pykfaTD9O18iiJW694QpRtUdonCwOXplY3azRu1\n0fkAAAaPSURBVEk72LDv3W0eqYi1Mo//kgXJKQrVPa7YEaN2C3EfZzAJP71lRSEMQVqK2W+D\nQEwEaSlmv58IMRGk5bidadkNo3FWpkWQFsS6+7+0IbMCEKRFsWxoljaJUwCCtEKLu6ygAARp\nhQiSHkFaIYKkR5DWiD6SHEFaI0bt5AjSOuWcR1rkHBZBQloLbQ0JEtJaaP+MICGppY4YEiQk\nRZBCFimwCOThEaQqBicIEtJy7SNVMjhBkKDg+9BVi9f3/iwYQUK40Mc3TL347e9SESSEi9hq\nEKQQpX9qeBFzZydIIUr/1PAi6s5OHylA8R9b1eTDyXGDxKidv+I/torF2DHjthrMI3mr4IOr\nVoydvpJWIyaCtDKRTsOqaDViIkgrU8soWG0I0soQpDgI0tpUMpxcG4K0NgwMREGQ1mf1AwMx\nECRAgCCtC61RJARpTegfRUOQ1oQRu2gI0oowhxQPQVoRghQPQVoRghQPQVoT+kjREKQ1YdQu\nGoK0LswjRUKQAAGCBAgQJGCa1ekwQQKmWA7QECRgiuWUAUECJthOYhMkYAJBAgQIEqBAHwkQ\nYNQOkGAeCUiFIAECBAk5LO4qdIKE9BZ4XxRBQnoLvFOXICG5JT47giAhOYLku0iBRSAfguS7\nSIFFICP6SJ6LFFgEMmLUznORAotAVswjESTgE0ECBAgSIECQAAGCBAgQJECAIAECBAkQIEiA\nAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAoNElAZj71cH5zCCw5DtROqqdYEyQ3V\nTqimWhMkN1Q7oZpqTZDcUO2Eaqo1QXJDtROqqdYEyQ3VTqimWhMkN1Q7oZpqTZDcUO2Eaqo1\nQXJDtROqqdYEyQ3VTqimWhMkN1Q7oZpqTZDcUO2Eaqp1TXUFikWQAAGCBAgQJECAIAECBAkQ\nIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBPIEqW1M056yFO2n/2z1Wiq/v2/b\nXoXLr/u91rV94lmCtL18RpscRfs59DZrLZU/3L9ToVfh8ut+r3V1n3iOIP2a5tAdGvOboWw/\nB7O7/1hL5f+qeN22vQqXX/dHrav7xHMEqTU/f3/+M98Zyvazf9a1ksrvzfZ+XvSscPF1f9a6\nuk88R5B25ti9HHOKtzf7+4+VVN603W2X7FW4+Lo/a13dJ54jSLfPyud70TLZmZ+vv/7u+cdK\nKn94r+n5r+Lr/qx1dZ84QbKxu/Z8t11Nla8wSF0vSJV94gTJhjH/uu7Unk836ql81UGq7hMn\nSPZO5yHYeipfdZCuKvrEc9SuqeKTGXCucT2Vv1WxV+Ea6v5auVpqnXPU7lj4MMyA87asp/Iv\no3bH56hd2XX/DFINtc4TpO/LxMCPaTOU7acx5wtULtuynsrfdslehWuo+6MdrewT58oGG+15\nK54uM4P1VL7GKxseta7uE89y4rl5DG1W4tRcanw5JlZT+ftJUq/CFdT9VuvqPvEsQTpdLufN\nUbKvc403+8ePVVT+HqRehSuoe7/WNX3iZQ+FAJUgSIAAQQIECBIgQJAAAYIECBAkQIAgAQIE\nCRAgSIAAQQIECBIgQJAAAYIECBAkQIAgAQIECRAgSIAAQQIECBIgQJAAAYIECBAkQIAgAQIE\nCRAgSIAAQQIECBIgQJAAAYIECBAkQIAgAQIECRAgSDUwg5tp+F+RBduiBgSpeGyLGhCk4rEt\nakCQise2qMElMsYcd6b5vvxD25j2FqT9xjTnb//emt+/P3/NV75qrhlBqsEtSI35c07S9vzD\n7vKvu/OPZtt1R9P8/do0p7xVXSuCVINbkLanbm82XffPNIfu0Jz/9ef8j6et+flrmv4y9m3+\n5a7rShGkGtyC9Hv7cXf56ef647kFOpldd26n9pe/kQFBqsEtSPcfb6MM1x9vuvPJ3V83KmMt\nV40g1cAuSF1r2nx1XDmCVIOpID1fRYuUEUGqwVuQduexhe73+ePV7q+PtM1Uw9UjSDV4C9LP\nc9TuMoDXXQYZ/v2d2H2bfeaqrhVBqsFbkK6TR1+XHy9TSqY5dqfmMo/EyV0eBKkG70Hqvl+u\nbDBff+n5ul3ZwMldFgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBA\nkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBA\nkAABggQIECRA4D98+kw4ODYltAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(coredata(df$TJR))\n",
    "lines(fitted.values(r1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x49ok6VQOQkadpmDpfjriZEO1+AZZZlb0QFsMuJs7XgW3ZFdvmLPJdTvhdiWbhW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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(residuals(r1), type='o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A interpretação econômica da variável ajustada da regressão é a tendência de queda da taxa de juros real para o período. O resíduo da regressão mostra a variação devido a outros fatores que não a tendência linear de queda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4 . Estime agora a regressão de tjr em uma constante e uma variável “dummy de degrau”,\n",
    "com valor 0 até 2006.12 e valor 1 dali em diante. Apresente um gráfico com a série **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = coredata(df$TJR) ~ coredata(df$DUMMY_DEGRAU))\n",
       "\n",
       "Coefficients:\n",
       "              (Intercept)  coredata(df$DUMMY_DEGRAU)  \n",
       "                   1.9059                    -0.5385  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df$DUMMY_DEGRAU = 1\n",
    "df[index(df) <= '2006-12-01','DUMMY_DEGRAU'] = 0\n",
    "r2 = lm(formula = coredata(df$TJR) ~ coredata(df$DUMMY_DEGRAU))\n",
    "r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ulRO6tqHh73Why3SYNE42xh0ndrA4PU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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(coredata(df$TJR))\n",
    "lines(fitted.values(r2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eC4RjIN6VGkD/+j4xJFrKcqLVJn1w55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\nBEAkAAH+B5GFwYbAXZzxAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(residuals(r2), type='o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5 . Aplique o filtro HP à série tjr, usando o valor padrão de “lambda”. Salve os resultados.\n",
    "Em seguida, repita a operação com “lambda=10000”. Salve os resultados**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "library('mFilter')\n",
    "hp1 = hpfilter(na.omit(df$TJR), freq=14400)\n",
    "hp2 = hpfilter(na.omit(df$TJR), freq=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** 6. Apresente em um gráfico as variáveis ajustadas obtidas nos itens 3, 4 e 5 acima (aregressão\n",
    "em tendência determinística; b- regressão em dummy; c- HP padrão; d- HP\n",
    "com lambda menor). Comente as diferenças e semelhanças. Qual procedimento você\n",
    "julga mais adequado para captar o componente tendencial da tjr?  **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GPfWapA8xCRZA6R+uPUUpE8TQBEKpL4\nNukNqkOk7sa+84dQcZwhEpPNF4qYhEg1kyBS1zCpRKRNyBIp1ySzSkOkSkjZJg+LEGlpModI\nTdAka8zHLZK74wRHk7xNihepe/TlgVMWx0WKd5P0ciNSTSCSXKniIi26MwmRauJ5RNoQOZEM\nkyIPLY+LxHMpymF28iKcsHCRLqKnj5wh0pNliaT1k2Ii8aSkkngukQ59Yl+jD2+aS2nKaCY5\nRZr+RkVaUjbYmGSRFqbLZKVIr0r2/glHiGAyo5Jwi6SZ5BBJ3xwRkZZuOdgS1+EzbYFtWCnS\n7XKWvcl8HiKYzKgkYiIpjybD/26RGvsbRCqBJJGU5/UGrG7aLRm1+3q/dBOFx6Z4SBXJ3Lc9\nIo0mucbf0kQyRxzSCgeb8odFur1qqcPX5u0mklGnRUSij1QSTybSEq7q9K97mtLP5yl8tbis\nSINJbpFio3ZT1ozaFcQfFml4KFlL5MFkon2k8Uohp0hN7DySEQGNSuHpRPq8tDvXJWHKhvnN\nqWtLlTZq1wwmeUQy3wRFgmJQjlfORDtd/r1WpHPXPUqZ/GSLGqlxn0eajc/dXxpnrohUK4ki\nTUfaskX6UOfHXeYfKv4kit8+0menm1gfyfd2JtLDpHmuav7OznOfO/5hKSkijbtB+SK1czYk\n98HP2qjda/BEbp5Ixhe2SI09F8o8g3kTYFw1RCqNNJG00aiyRequAG8SB7O+ro/zSKfLu9B5\npMAX9nfOW5OiIvlyg6N5MpFe+xrpW72KFanZRKTmruYmRURSzmRQAotF2hiZPtJvn0d01oYt\nRHLdmoRI1bK4j7Qxa0ftLofPImR+Mo0NzL50TM+1WCTOI5VCqkjJ/Q6x8mQu0p5HUpd/izMJ\nBs4UyRgbcOTRzgc+m6O4W3BawtlHMiJAASSK1Ox1En21SLlx5xWGTnpJvGMDrjy600n2NjAm\nW3eP2vmLDceQLNJOHCWSSAjLl+kctk8kdTdyV/p/LpFmxzNEKoUUkfbkeURS01C8TyTVDziY\nfZ+pfRePjUil8GwiXU8HzyKkVS9q/MgrknmtULpIY2VXxlaDxSJt3VVaKdJ1Sbfm9qbUuX/4\nudhgg7Jeq0AfSfXnZZeKpF+whUllsEyk7QfvVoqkFpw/unWV16VfUKBUM5HU0MLz5KHMa4US\n+khGAkQqh4UiJafMZbVI6ctdW+luH6dzfMF0kSwp/A8NHbtQsweQmZOtO2JrriJSKSwSSVn/\nb8Dqpl36LEKnbsGf0+uPkEjGfq0ddOYiTWeYnI9N0iZbD5QGkQriyURqzufkpzAP7tzO501E\nmprBDpH0bD3TGCeIFNINdiUqkt5tr0Ckz/TBhmkOvNfzBiLZrTPjG/N/t0nOoFpWqkGkclDO\nl9Nn5uhC8X2k9wWjdtPNfz/qvIVI5uIBkdwmBbIaG4aIVAoxkcxvih+1W3TV93Vck8+IeBIi\nuT4Yv3CZFMpquhgWkcogLNK8LVf4eaRlpfu+DK9+3nYVaV61R++pcH6ISMWwVKStWd20O3Lu\n7wUizar2+4t9jEKkmngykZr3I+f+XjIaPdPm3lhqKVe6uWuYVATL+kjbs7ppt/DOh+UhwumW\nhx16PdYMXf0FenbNhUhl4hpKMr7ffHTBDrhukWpFUvZcd/qVrohUPDGRth9dsMPtsshWIVaJ\nZM51Z5xtVVZq/R0ilUBcpJ2pTKT/RLm/yOZnsf3v9HdBJNEQ/trb30ZW2n/GA2ZdNZJVNS1a\ndUTakOUibbzbVt5H8ovkzWcQ6WGa/oBZVx8JkQoFkRaHCKZzD9gEJwZUejr7xKxdkSFSoTyb\nSD1f58v8wxWsEMlUwaGEtYh9iYN7vi5EKownFam5JTyNYmUIZzqHSEYGcZF8N1U4l0ekUnhW\nkYTPfeWLZBrkOiE0WyRkkpUBIpVCgkgq+FYaIZE+wg8OkwixbEn/JQrzvAMmIVKhPJtI01jD\nu1iRGhGRvBfNOfK+pxRkECl5XAWRNmSNSJtc8yAk0qvowyjWHD18496ukbgB3ywODpEWXMOF\nSBviPkj6kwTaKhsUaLNFdgzh+51CInUXC+mj3kMmpkjK76kDRNqQFSIFFpEq0GaL7BrCWXM7\nekt6qm6OLjX7sW2RXMv6QKQNyRZpyRbMLtBmixwfIiKSPim4rgsiFUpcJPvDwkV6fz3yyoas\nHF0/pT69PiJVwLOJtGQWocwQoWTpUaMiTbcnhURa1MLGpO3IFqnQPpLws2NdIfyJlgy/xEUa\nb0/SdTHTqGVBEWk7los0VklFjtptdBdimkixpLYp1svZtrgPfSTnqN1QP6VXg4i0HfkiLWrI\nZBZo+SKXnWcR+t//Zmn8a7BIpIdJavx8fh6pWXw7LiJtxxqRNmGlSD+nvWcR+l+PsEidOnf7\nc0QqlPimqEuk4+5H+t9QOUmJ9ODuXwyRSgKRFofwJxorp4Rc5iK5Y9z9Ii0GkbbDtWF8t5IF\nFpFjpUgbsWzUzudSjkjDiMOCcnhBpO2Ybxn/zc36B5tN0lWxSPqv4qycskTqRxwWlcMDIm2H\nQyTzc2eCDaeNrFqkOYZLHiMiIuk3VSBSqXgbbv4esJrJtmmBMhcp5xKhqXLKFElNJrnTcB7p\neLJEGr8r7zzS9GExIg34Kqe4SP3YnUKkcrFGvJ5HJFlkQqjufNP8CoVwDNWP3SFSwWiDCn2/\nJ6GPhEj52aj5KERMpM6kuUjmI2oTQKTNmLXaZ/cuB/tIiLQ4m/6nU5pMKSK93G2R7IemJ1CX\nSDs/vWEd81FuZa1BcNSuQJE+Xpvm51W9yl4oJCaS0WLuK6cUkX5Nso5cWsvhGUXa/XlC63CK\n5ElhfKK0mak3KlHWIp9tuU7thQ2iJm0jUk/oYogp8cvdEEnP6ClF0v5WQLZIvi8FS5S1yFn9\na77Va/NPncWK1GwsUvsmeHFRd+jqW3dWBk8qkn+sq0zcTQVPCt8yW5UoZ5G2QvpWV+lWgXgf\nyZO7W6a+/fZytz+bvksCkTbD3Xl1J3Ats2mJchZpV+CiPgsWyfEzm+/cw3qPNHOTFrWAECmT\n+LiH2cIIzr7m+qg8kc7q+7OdrbjUpl3j+pmduVvDel0a/WohzcjnE6mkPlLKuEe0oLWJ9NnP\nVqzaWkkOSZEW5K4N6/VpjDrJ8bCYIFWJVM6oXYrTTydS83Fqe0jN6z+h8jhCiGcTy10bI3dP\nC/6EIqW0p/Yh6Wj1fCJtg7BIjvn0Q7tN+83Yc3KZtLVIR+/Th8bPE8kuslekrdqwf0AkxxNe\nwg0ZrWn365LDpG1FOrqVdXD8HJGmWZ8ix8fyRfoSffalrEh2lrMLHB2LabXWfTZGvrFIS2Js\nQA3xbZG6v/Hjo/5Xtt5dK9L10Icxp2QzP8LFBg06kaatcrfHyFOLl2XSwhENcY6OnzFqZxY5\nTSTpenelSJNHxY7aZYs0JRlbd71LiLRxEZadRxrexa7O13aHWKNkOStFOql/zVn9/JwLvdbO\naU2SSEYarZ8Um7pIpzqRlFr2nIDDWC2S+FquFKkt0PtvbfRd7AlZ57EnoY9k/NIv91mCFJfy\nOkmH9VGU3nMo2iMbs8i1ivTZTqRfbB/J2RpOGLUzf2nTpP67aOWUKZJw6z01bFqXvUjSDgEl\ni3T5bdr9qNfmq2CRnG3u2DipXZE5r2Dt8bqUeyLpkPM42r519HmsDLoJBcZDgPepjWPrr7A+\n0uN+pHM72PAmVqRGXKSsxawDc8gkX+VU1aUN8gfpA1C6S7MvG10k4Xp3pUi/HaTfP2/qcZ2Q\nHFLrp1aIZB/WXlLmuzNdqkOk4cEbB4skWA16ahtDJOl6f61I23C4SM6lYvPddWiVUw0iTRcF\n9H2IY5p1QhXE3cCO0RgiyfLsIuXk5NXvrqeIbfVfl6oQafj7aO08zqwf0kPT/mZutlGdsWq1\nZEKkFfm4coo5kCBS2gH0vwXnnA5CG2FoplbegcWYChNKPvvpdWWMzLQvEGlFPvOc4g74G4TD\nNkk81zLUSBku7dXCskSyPt2NRSLNt+B9fp5PW4nhW0RakY9DpGiEQM9K2ySxXBqjj7SsYtrv\nVE6VIhmLNPNbXWY/39TkQ6TMfJxDN5EQoSEKqxUeDm/1kZIbenteXGDsuoeJtKSPZBdyNqjQ\nzCv0+/AoRkTKzEdaJPMxs8tE6onLFMxe+kL7/uit78nLzl+LFqMvxAKRDI1eDPRv7ndEWpOP\nuEi6Sal9pDnhyilQxuG8vdAv1A3STXuY+7KAXVqaxpQYySJp1VGnjr6kKdPdEikSZiF/TqR1\nfaSWRyshadeKDn97ZAqJ1DTa5TArsaqB/rP56u/Y0uwDpfaRRo1GZewlNZfud0SSzDvuQKSz\n29VJCXty0nkkR+Xk7yMNPRmZnUDN/hpf2O/2MkmrOdzfj1tw8EireBwLTo7dEUk095gDsfMY\nru6ti7QTsl1xdJn8p6mU9W8VhiAViTT8QMNmMDpDzgW7FGp6QLDI72cWaZdFCgwRDh8rQJpJ\nKSLpzgyVk/LKjkgT3TawxhR8C7bJ2p91fkpJCERyho9VWSrJpCSRtL89oWE9rVm3m0h795HS\ngj22gGVRcMEX1bXuhlSItEP4cBfq0UZIKGOCSM6jvfIP66mxttqvj3TErYbRYJ1HvgV9DTyl\njboi0g7hI2MRzdTaDpEpkvbaIZOSu4XVNWo3L04fdH24JaS0refVURMUST0qpXHwDpF2CB8c\nNOr+SzBpvUgtzmE9oV9oqtzCIu2ACv0GNg+PfPn4FleDe/epfSzGc4uUucPFBsc74t2kzD6S\nI7oynoIrTW0i3QMehUVSTW8SIi3JJbcJlCaSuvu25cDSUTsrwDzNRrdlVCaSt1k3LekXqTdJ\n/DbG/UX6eFXqEplOUkik3Lzi9yt1iURMclyR4wk4vpeWqS6R7kO94svHt3hfCz0c7OokwUGU\nHUXqSnzuJmYNz/Egsm6u7kfikhGRut+/HQGKmLRmYrup3M4VkZSpJJGi9xbeQ9VRExJpdLW9\nJO8+Nu7qFOmqrrem+bm2c+HJh3BmIi5SM12QFjFJVKR5M0SqpVeOSNoMEh7u3QmhUD7epcdK\nrx0Hv6/YQTxht1+kW65d8KRu7eubet0ihDOTDUSa8g1fLSQo0uNOB3fBVrtUkEhD9IBIL+HS\npYjU1mmVizTsCmn9+XVs1Ucysg8O3v2X1QB39pHGW1h9Lq2onOa52kHypiNZWAh93nFfuHvz\nEtmkSSI16kXdqxbpbRDptEUIR0D5UbsxVf+/1ySl/suKPxdpqo2sW1ltlro0Vn51iHR/eCQi\n0m9G92r7SJf3j0/VPm32dg2PNkhttU1PyI8i+c9o/NfkrItjiXFFIiI1CyunckQyDnqeivfe\nD14LidTf6lehSOMTyZQ63bYIsStjIT0mqb6PtHhlXAtYx+qEPNNmhzBy9RdhJ5G01rgj3n0Y\nrssWSWmp1MOkKs8jfX9/fFwujyGHa9CjykRymNQ/aChJpOherH04HKrTfqB45VScSGMdMY93\nH88eyYjUNu5cafLWdE+RigqxHq2Qd/PMxrg7SIo05LlApIHo7BDFiDTtyLN499BZWEdGrq9M\nkRwm5Z+iRaR8dJPu87s0VWIfKU2kcRfLEKnxVk7pIm29Tez93w53D56FDWSkf2V//mI9Qa7x\nSJwYdvtFCgwhgFFKzaSxP5M2aufdi92tjDyRBuzLyCNF0N4eK1L0aixvRvpX88+dT5DbyQqR\nX3SP80hbY5ZyOmROmyPpPJJnL/a1MpaI5FRRq5ymkhYuUrpHC0VyP/eqapGUjkSIfBILYB80\nh62tiZSWjbLea//Nfyb3x86Mww3+X5f82cyLdKRICzwKNUOdv4XruVcViXR4iEDw1A7nvD9s\nmKRSr/52iqSc75aJFE3qH9I7XCSdxEmbppyWiOQwiT6SYPAMkdRwh5I5ahfPZhuREg6v7VfB\nUQjtnVFdyLcZAiIt82jeTo3F1Uxi1E4+drwM1s7Wvh3rpG5jpN4iq+wPdhSpx5IpJJJ10aTM\nxvKLZA+srZ2VcB7X6CZxHkk49mKRHn/NUdoVIpnGKCupvEgtWuUUFGn6K3drnGocP0WL9eij\neMAkkbRrruyhuzwQyRd7oUjDm7uu0iqRjOO+lbT/mzL2GUri/u5/s2EIo4xq9uGeIsUDJoik\n/bZqHiMLRPIETzmqud4o/eTsGpEMT2yR2v+iB+f40dv/ndlz8omUftCJ4hPJ5VHs6BAXafqr\nHFFy2FEkpZJHuNiQOi4AABgsSURBVI8VKbW54hFJa9/951wTc+X9Is0+s0TypjYihX5qpaVz\nfqOdbzpEJPu+SRmR5nXqepN2FOmjEpGiTaYxmeNdf4DrKyWXSLanuSKl7cTho4LyptHeaTOS\newqzgUj9NPlGCpW20nkiLTlTFcpz20U6vk/nrUPsirXrGbtjVyk5RbKWdbVnPJFyRAqmUd40\n83dTS8/uYUh5NK1fH8EcTWumI1xmQHtxbRVWV0l7itR8RyYPEgixJ7PmkH5U/62UlEuk2f6/\nQCStNZUoUiSR8qZxaKW0ysmYMUBi1M4Sqf3jugxuzXTNHv/HQ19Onnb5tl5k4EN9bx1iR4Lt\ni3bWO5UqUreEPz+XSEm1gbBIPfNnOa1mXJlRppe7XoipkNkBtd9L13FqQxhv83LfepECQwgQ\nbqh3zbtUkVL6MrZICQdnGZFcygpP+jqEGEv0cm/cIq2LYFZtRo738Tb2HFcRKZ9AKbuvHs07\n91fK+X6RSEkbPJiv8qeJitQTlyltr7RFerTrNhRp/nlvkspsriJSPr7dUxtdctyO5hq1i21l\nj0gpZQztFcqfJtDOmxFyKXWvNERqlO1RWkM2IUJIpIdJKjMSIuXjLKW55/x3d6qkL7mpSCpY\nI0zNS995pGi6Hu/sEKl7pSXS+OT4KUFWPZFQFF2kdhLXzLoPkfJxi9T97f/773efiNwkbYnk\nsGydSHnfukRK2Jdtl5L3SlOkF9f0Pqk9F186T/H1D/RpXBFpN1ylHDdDt9Uew3ZhlfQD5Wx0\n9zCRjO+MmLHIRuWUJdJsJoUlhGx3KmZ8dEekA3A0h/SJHLsbkh7v77OHb5uZjNP9RZofixse\nkiIp5zsvD5cWF1e55vZZwuIejpl0NIk+0o5YxexGGfRTfuMZ2bv3YSRqPIgGroApWKRQe2us\nnFK3p3e2OXe5Al+n70FzkbJ6Y4i0grHvoHWMxsnuH0xnZO9398RsSt8zdxZp2ZLu0LETWe3X\nS843xeqjjUXqRu44j7QvfbNs/NO/1R6/Ylza4OwrGW4sFEkl71fLcYhk1LXTp7GMBpeSTuBG\n23WbiKSZkzoPpS/wtosUGEICbcfS6hP9eGZdI9SqZG0n041IH2nabXcXqbshY/6IpoUH74hL\n6/pHLct7ONYIT6ZJiLQCqzXmOBrOLra7P1zSPrREcrfPV4mU92M6K0XH/U3LW0H+yullvUcZ\nPRx7hCfPJERagS3S/Gjouo/ifr+b07Iai7na59Mnh4k0xrX30/xzpDOXXqxpSMIl8rK0h2Mf\n/4aHxywDkVZgiuS6Sst5i6xqz9IO934qx86pp1WqLJHsL1ddbDBUTo+1fLFv5AuXSIxZQyLL\nJERagdlHsnqtD/4L8OtS6Os/xsvL7y9ydCF6fsvx4vo8ui9k7D7bUpVIQ33iqVJcH42tiPs9\n1JgZJA3USCkF9H256JIbsyqaukrBTNKv/H75rZfuZs9ptxppWrW+vDlVEiKtwOzWZIjUosnk\n23WceXgjpqVKviy7T2em18f8vXkkhnh41Dwen9cYPSdP61IaNV/Fu1psEiKtQAXeBT6d73u9\nS1uKZFcOs85OKIvpcG1UQzGR+r/xflzbPbqPmbonqXQ2nYWYVbrL6yREWoGYSE1XMW0jknM8\nI5B1sAhWxRTyxFgkGKIbZjBCzYfIXWshih6/Pa4tMwmRVpAikuNj5Ut777CX9V6zvEAkuyi5\nIjWNdU3gepEGj1xFMiepTK1F89Djq8VVEiKtIE8k5fpw5OXlRRsb9x6Cl4nk0MFXOmcOvlWV\nEOnl5THvlmMShZ5hiDy5zJkYIi1u3CHSChaKpA1KKPMjk5dOJn+CRhMp2GvwixQ7uhuTzM/T\nTZ+u7SP1wwxWH8WBNq9eKL8VaPERaVdSReq66UPtou0z/ja/UTH5Ykcn6giJFFpS+9KdbtGo\nXWBrPq48vFvpPbk1SnrqIjuCttaLxxsQaQVpIg23Gw2J7INvaGXvVrfJaADFew1GzFl54wIG\n0k0rFKoRtZrGQafR3U7vLdMQcTOZ9Hp44XgDIq1g2qkD+4t1BZ6WNrHNP7X09EO20T0Jd1NU\nE6u5nIulbYbkZz/MeeymyVepWmshVzn5rm5cZhIircCQI7wzN9OxbqlILXpLL0ek8MHeU+Rt\nRXpZ5pFnLVbL5Gl/9lVSukmItAJxkUJ7+8so07DwIpGWsECkwIrP89PpNOrq2WCjOJRJx6rK\nydNAHaqkZJMQaQVLRDL7K84+kq/9NXVHtPG8ZX2khaQvlynSVB15G532F9EwWTKNW8cnUqpJ\niLQCzZH4KHB81M69++oDZC19xaRS+j7ZIiV3qfJE6nZO7bIol0jWF0lrsbhyCom0qEpCpDWM\nzbWgSKNB4fNIngaV3s/pX75oXaak80jLSb40fLlIw932xuWFs0zGFvGCduZIukxBkZaYhEhr\nSBLJ1dh3JXbvMfqnekWhn7WNlG/LX9MhUnj+43HOirvxlVskNZvfLJ1Elzw/kZoKiUjbM22F\npGfSTwvliWQdoB/t+OhZW/+v2R91fdglcC4+E8kaordymDS6N54k89zzRGrSpi7ytGI1kdJM\nQqQ1ZB3xfSK5c/Ptadoe7HdJGf9ZzC6RdX8/uybdyHwu0uzv9P9Mo1lKMyNdojW7RNil4ETG\nySYh0hqyRXJXSc6Do7/toX1m1yLGslaVOabtOltBtPTe9VCzD+3yDo3RsQDRlW5mzbqVu0Tq\nvHpj9OFFqkmItIYUkWYHvEBLxXmS3dv2cOThbpUpowFneRLE8sm9Hsr+sJmL9OLW6PFt9DyS\ngEgDqS4h0q7ERXJosLjJ72t7+POYd3hc6iSWQY0+maMb6SLpcRdNXKf9vnK7RFLlNIVLNAmR\n1pAg0jyFzH4RFMkIbjftZl8n5tLYN0tNWc9SK30RbS+MDTPaoX3tPgmCLlkixU1CpDVERbIP\n0MpaJn9FVUIe60RyVi4P+ipuylpfatj351VgdLTeVYjN7ixv0Ssn7wVJaSYh0hoWiDTeUXCM\nSK4KLFukFm9ny93/Cg/TH83jBlyj7puJFDMJkdYwSeE5co47Y7+djhRplnCVSE03XWw/Ph4e\nwChaog5l9Zz0lU6qkhBpPaEbVXttBnueSaQxT7cnw2SLFVikr6trKrAUkxBpPaEnypuKKWWm\nWrGeu4kUzr7/Z10Q4bg+omyMg8ZsWC+lcYdI6wlfV2lOX6XKESkWfIlIGp09Zr0bHDEoYWPP\ntmD7YnIp4XCASKtJmCdqU5FSwuaIFKhnp+9dNZ0ZOTqGnfIjbDt41zjWtXs5VExxkxBpNSkT\nro3b6S+KlJBNpCARFQWYhVCjvf/r5vePZZARc/kiBYaQQ8X3Fe2epD8nUnIpw0E23ylmTyI0\n1LrHLi5CpNWopENm8BrjzKixXLQW/44iaYcL/dt8keIV/gZYd4JEG3eItAJt2ra8RvwTizT1\njiLhIsU4TCTrf0TajISJREMLexpFyRksEkk50iUGzxNJO7REfKxEpJhJiJTNsIPk/ITGnpYb\nPbFKGeLZC2wokvk+3O6Ni7RPH8kR14waNgmRchl/6eyfcN04VMLSZYgUOWSkiBRWcRPmPxki\nbcMKkUTaKuWIZCZZulIJIq2tvXNQc3uDJiFSLn9FpHD2O4l0CIvsRaRssvpI2oNYdxTJ+R6R\nJEGkbDJG7cxF1q0lIhUFIq3AqF6SFuj/SvSeM0Ra8m0Tb9ogkgYirSWjHa0kes/anOHeaXiS\nShPKP3rZtkekBasXS1jJvoBIa8kTSSCu0v4P358bLk3w62Ai5RIpXKSlpahmX0CktRwukjfL\nVY2mlLJ6RZot6c8Fkbakkh/vQU4fSSSumZkjUwmRYudSXSI5irRWpP13iKVtb0RayyKRBAYZ\njLzSRPI8TjmcfR9DBcrrGWp5ApGWbyhEWsvCA1fCGEFqTkZ4ZX057eS+nSKhwgo+ZfqpRdL+\nLlkiI8im1CRSJqsrp0AfybwmdkpgqBsLbU1i70zi+crXR/I9PzxcjqRUsmR0ZhHpIFZ3lwKj\ndkpPMO4UVsJ4aEtFRwKfSLMiKeenSRwrUnKzAZGOIeOY58/L2thm3pNIZsCEyLFCzq/qGJ8b\nbe9/yi5OMoeKlO4+Ih2DpEjhvO1ISyJH9n1bpOAprdw1PrKPtMB9RDqG/UQyd4qFIoWPyDOR\n/BnXJpKx4unHnGVBli9SYIijWd1HiudtdqJyRHKPD2hxlJ5GBY7glYnUrQwiVcCWd33ad7Lr\nE0Qs6SNF4zy6Pv2KdCPuUyA7aU19JD10YnREWkn+2aAt7/pMeIammEjjy0Ein0h5h44DRVri\nPiKt4ojZBPJZdB4pJT+rxaaaeb9JjzbXO+FgcqhI6ZsXkVaxZU8nFnrt/UwCRbBFUt5iuT9M\n2U99ddw+cB5pF7Yce4tEXt1O20CkwH4XsKtokYZCRH3adQt8vV9Uy+X6tVWIfTlQJDPucSJp\nfaRQrp5+U0JJChAppebccQvcXtXEeZMQe3OYSAKBJco8DdTFbp+vWyTtbzhNRrbLuarTv+/H\nq5/Pk7puEWJ3juojFSTS1O4JtX9qFimpnDuKdFLf4+tvddoixO4cNWqXsG1Tpi5ZXYz0TPwm\nJfQ+EMlYTvneiIU4gP3nAO3Can9d36ZNXbK6FCtFSjoMIZLFM9ZIhxHrkbhFU57Xq0qRmNQZ\nMeUwdLhIBfaRPn8er56nj3QgwR6J5yBanEjbLinBeMAqZ9SuOWujdq+3TUJAByJJER9H0dNl\nZJ3D1/VxHul0eX+S80jlYD8B1frf8RaRUqOLplu3SIEhngr3vd1F9ZFWBEGkbBBpGXNt3M16\n5Xy5RXzZzBEpE0RahLMhF5myB5GSow+vpM8miKzV05xHKoGkEx1WgoNEyjjtVoZIsZG7ckRS\nOhIh/g7JIunHV/kCJIRPGEd2ZV6CSMY7f7qMrDcEkZZhbOW0S96OESkndBEiRY9ViPQMaEf6\n1IuwjxApvea0lkKkTBBpKY4Jip3JHK8koseznM/Kk9qCP1Yka90Q6Y8Q2eCyIplzfAXHtIx6\nUs0+CUYpQiT6SH+LHUXSVYiKNC3Rv1kw0FeGSIWO2h0e4knZUyTrbyDH+Rjygu5SGSLFmqI7\niqRU8gg3IuWgPRRphz6SoUKqSLPZWCsSKSVZRs7L+UCkLRmmV00ctVsfT/8/WST/J6GFEcng\n+xSe8kQgxB+m26FV+JE+B4nk2BuX9JEO3R0KFKn5Dt/OJxHizzJUROIt+UheiYMNs3pyySSm\nx4sUL8G+gw0f2t3mG4X4q6jx324iLRi1cwmePokpIuWCSItR0yZP6KwIxUw+j7QyzFY5J0Uf\n/8STZeS8LYi0nPDTIMZEWwVHpLyctwWRlhN+PtGQaKvgG+aNSPkgUg59SyvpxILwrSpLRFoc\nGJGyQaQsEkbCVGrCpaE33GaIlA0iZRKtaOwxa7HAiJSX87Yg0lYYu4Xo6VlEysp5WxBpK0oS\nKblThUi5INJWINJSEAkclNRHqmQrp41IItLfoqRRu0q2MiLBnI3OIy0rQ/S+7aJAJJhz/C87\nv0u2cBAJ5hz/y0610fFlSUIllRSR/haH/7LTiOHhRUkEkWDO4b8sIq1ZpMAQf5TDf9nlIh09\nFTwiwZzjf9mxj5RWFPmR+qUgEjjY6KdNrzZGMxJF0v4eAyKBg01+2mXVRsp9U2Na6/8DQCRw\nsI1IOVkj0vJFCgzxV9nip83b2xFp+SIFhvirVCYSfaRVINJmqA3GkzcViVG7FSDSZkSfT5KV\nqfZ34UIJ6TiPlA0ibcYmV17nPmS5ChAJHGzUe8+oNmrZyIgEDgoYBmtquva7SbyaCZH+GIi0\nGEQCB8ePJ1cnUkpREemvcfx4MiJlL1JgiD/M0ePJiJS9SIEh4EAQKXORAkP8UY6vjR6kDSkX\nAiKBRQn9oweIlLdIgSH+JCWM2A1FKKAUiSASmBRxDmkowfGFSAWRwASRtgOR/hCItB2I9Jeg\nj7QZiPSXYNRuMxDpb1HMeaQiiiEIIsEBIFLeIgWGgEMpo2IUBJHgCCoSKa01jEhwBNWIlDo+\ng0hwBPWIpP2Np8vIelNq+ZUhl1pESj6HjUgAfhAJQABEApCAPhKAAIzaAYjAeSSA3UAkAAEQ\nCY6gkKvQ5UAk2J9i7ouSA5Fgf4q5U1cORILdKWfuCDkQCXYHkXIXKTAEHAci5S5SYAg4EPpI\nmYsUGAIOhFG7zEUKDAGHwnkkRAKYg0gAAiASgACIBCAAIgEIgEgAAiASgACIBCAAIgEIgEgA\nAiASgACIBCAAIgEIgEgAAiASgACIBCAAIgEIgEgAAhQqEkBlZOzl8uIczjOu08ATr1vdq1Z3\n6d084zoNPPG61b1qdZfezTOu08ATr1vdq1Z36d084zoNPPG61b1qdZfezTOu08ATr1vdq1Z3\n6d084zoNPPG61b1qdZfezTOu08ATr1vdq1Z36d084zoNPPG61b1qdZfezTOu08ATr1vdq1Z3\n6d084zoNPPG61b1qdZfezTOu08ATr1vdq1Z36d084zoNPPG61b1qdZceoBAQCUAARAIQAJEA\nBEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABKhepI9Xdbre\nHi+vJ8fL7FnRC8C9br+fD6tjfFoVsVWrbrNVVFQn18fvfWq3w/nx8rUxXn5Xt0Um3Ov2WKfu\nhfFpVcRWrb7NVlFRXXyrt1t7GHtrmi91+m6+T+rLePmtLkeXMRf3ujXt/91WMz6tiuiq1bfZ\nKhfp0pW//fmv6vP31T/1brz8aP/UiXvdftfo3O9t+qd1EV21+jZb5SL1tD//Rf00/aFMe/mh\nPo4u3EqsdWvUten3Nv3TKvGvWn2b7SlEuqlzM2yC9j/t5UV9vv32ZY8s3TrsdWu+zbfjf/UR\nWLX6NlutG8Hgo20e+ER6cD6yeKuw1037v3aRAqtW32ardSPo/Jwe7QKnSEr9+z30XatrKQzM\n1q2Zva1VpPCq1bbZKt0IOrfT48DlFqlPUuUYceNat/nbSkUKrlqfpKLNVudGMDh3v/Zp2iKn\n2R5W6c7mWDft//lq1kRw1RrXu6Kpp6Qefl7PP48X3fDPzzRq96MNZ1W0RTRc69ZijNr9VDlq\nF1m1xvWuaOopqZvPsUP6/jgh8amuxsuTas+e17mzOdetpd+/rE9rIrZq9W22ykX6mQZ23Fc2\nXNstdOvO+lWGe91aqr+yIbpq9W22ykV6U9NFWa/TiOn08nZ6vKzwoO1bt2Zq8bzWNkY8EF21\n+jZb5SIpbYvcHpcRPz62Xr7WM4qq4Vm3ZhLJ/LQi0latqs1WuUgAZYBIAAIgEoAAiAQgACIB\nCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAA\niAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBI\nReJ8nHfgGd+f1gPcb29KXS/1PIG1fhCpSBaK9PN4CLiW6qKUer+pnw2KBk4QqR78Ip2vVir1\ncOha4XOaawWR6sEr0j+tQhpEal/e1L/tSwUPEKlIWhF+a5WLOr0/3l9P6trb8fGqTu3jvs/q\n6/fvl3prmte+5hlSjU8MP78eU/w/CCIVSSfSqfWhNencvriMvR+lzm2/6PT79nS6/cr08Vho\nTDWK9PGQDXYAkYqkE+l8+1XhtW26nb6b71P74Wf74e2sPltL3pv3tvF2Vd/tMlqqoRX4ra6h\nKCAHIhVJJ9JX/+ryePXZvWy7QzfVDnef1Uf//6OLpKUaRLophht2ApGKpBPJfNW/VGPD7Ud1\ng3Pa140x2BA89QSi8EMXSZJIv2266/B5g0jHwg9dJAGRpkTUSAXBD10kpkiXdmyh+Zpedlx+\n+0htH2jsI42p6CPtDiIViSnS5zQe9xiaax6DDP9+G3bv7cj3tRvk/pyP2n0xarcXiFQkpkjd\nyaO37hzro4d0+mlup8d5pN/G3ZfqztpqqXqR3jmPtBeIVCSWSM27cWWDevvtGr31Vzacpysb\nplS9SFzZsBuI9AR8ei7z/lHcSLEXiPQMnN1dIa7+3g9Eegb0+5EmuB9pRxDpKfh8c3z4RsNu\nPxAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAA\nkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAE+D+WuHyu\n2tfuugAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(y=as.numeric(df$TJR), x = index(df), type='b')\n",
    "lines(y=fitted(r1),  x = index(na.omit(df)), col='red')\n",
    "lines(y=fitted(r2),  x = index(na.omit(df)), col='blue')\n",
    "lines(y=as.numeric(hp1$trend),  x = index(na.omit(df)), col='green')\n",
    "lines(y=as.numeric(hp2$trend),  x = index(na.omit(df)), col='magenta')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a <span style=\"color:red;\">primeira regressão</span> captura a tendencia como linear e constante ao longo do período, a <span style=\"color:blue;\">segunda</span> captura a tendência como constante em dois períodos distintos com uma quebra estrutural entre eles. Tanto o <span style=\"color:green;\">filtro hp com lambda = 14400</span> quanto o <span style=\"color:magenta;\">filtro hp com lambda = 10000</span> se ajustam aos dados de forma parecida, com sendo o com lambda maior menos volátil.\n",
    "\n",
    "Em todos os casos há uma arbitrariedade por conta da especificações dos parâmetros (ponto de quebra na segunda regressão, lambdas nos filtros hp, e a primeira regressão pode ser vista como um caso do filtro hp com  $ \\lambda \\to \\infty $).\n",
    "\n",
    "Um filtro HP com lambda elevado parece ser mais adequado para capturar a tendência."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** 7 . Compare graficamente, agora, os componentes cíclicos estimados sob os\n",
    "procedimentos: a-tend.determinística; c-HP padrão. Comente. **\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oQTUuWYPSqk6fXspg+A5PzTGEAyhrF/AJJahDR7zw5I/YjpQSq102cW6APJRgok\ntQckNQFpZj31wxlI+gWShNT/6dOrQHIdTslD0q+2mJC6S/hB6lfVB5K+BZlC6sddDkiOXHfb\nRrOkAamaGTh/SP212K9PFEj6NaJfW0DaBdJ4BwNJW5sYkNzP4jsvNnNvd+JEINknqH5PxoPU\nzDaxRuNTOzaXg6QjmCwJSOMbu3611ki6JiR7dqu1kOyZliENP6QPqT/6FyFZe6I0ZjEWNbGa\nSUAaLbufBBKQEoFk32hZqwmkSJ0PUne/IQ6kqW2xP8MvGiRjyUBaF5C62VZAqtp16a6kjZCG\naRFI5nzzL7XrL1aq2JCmVwNIYUWGNJrdKi4k48bBXsv2MuPp/tkvIAFJdogzQOoOlEVIw8Fk\nQZq9dT0EUmnOos06M9BEI0jDTfpcQNoyxDZI5fTlRnlCcl1mBaQBx3CZ0fRBkLQd6ZwBSF1A\ncnQ2SMNhfBlIk7NMQequGHtDprfe7JyQtHskx0KqKv1ayhCSKmcOJSANnR3S+CESkOxzpwKS\nAhKQmpODIWl/IMc1Q3kiSPaygZQWpOZQNCwp/Wu+kJqVmINU6XMuDORMk2T8mzSfJKQSSPOQ\nZq/Y00FyreI6SGrmSJqEZK12p2B+IFd7QyqtWcu5zdcDkqOVf8tjFlJ75Z8Akr16xhxjSPq9\nMSAJXyTKEAlB0m30y6i/9pBUaV5X3pD6qVL1Hyzm2Jh2TCCtCUj69yQh1Vd/fEjjrTkKUula\nbUFIq5Bsh9TuLiAZEz2k/g8nHASpOe6vBKl0rvY8pOkXf6cFaXZvXRCS67A3E4HU+ogH6bXc\na0HS9uN8WyENb9caQxp200UhNQfpUZD6P2RgQRqu42EdlduO8cMI0uu4moXUHAY7QyqtCwBJ\n9iJRhogHqaxkITXndjNtgmRdidlCUjO/SAJStLKD1A/YnzeCpPaHVKqDIFXjY69So33Ur8fc\nanR7aA9I1uXKzlK3MXPrCSTXkjOC1P4MJPNCQFo/BJDUNKRSpQCpMmd1rGd9mjgk98dALs8P\nJHMiMUjWWreHd9ldYjdI9gP+LCD1G1H1V2sMSN03B6ThgyJPCsm68hKEZBNpZpqE5HxMa51Y\nrYY0jASk5fm7b0BSqUEabpSslc4G0nB2UpDWGJGF1G3NlSHZMw+TUSE1ONZDqkWEQLI3J1lI\njt0+D6lbzWrFFTdcRgJS9yOQ/CGtuh6AdDpIpXWqCWlufwHJteCNkLQPUO3OUkBSDkjOBzgx\nIK2Yx3UxIBkTh0EyjryNkBy/exl+0hacMqSyP30LpKX70eVhkLojDEgJQupWq4OkXUmjo0+F\nQNLeJSllfEMAABI7SURBVD18NXeDAKT2l8LngKSAZEwASRbS5GwLkCpzVgWk0IvEGSII0tyu\n3g6p/c+ENDqY6nnPCKnbFbOQ+rubU8NMZUFaUwxI1exdYSC5FiwCaXww1fP2q1UakIZbr1iQ\nqhGkpSN4AyRzp54U0tweOyWk4Z/HvSEZh54IJGspGyFV+jKAtPFyV4WkSuN76Zq5n4wKSb8d\ncK11d0yfFFKl/V9bVgaQrKUAyTzd+kEKUr9bt0Kq1BiSdTFrkBlIbkntNhqQrGNRCFLVr8wq\nSI4dvxbSBh1A2jLE8ZCGNXBBsif7mWch2RfwgtTtgXQgNbNkBslcgdmXy54Y0hiPPj27q/eH\nNMx7HkiVPS+QQi8SZ4gsII0OEyBNDTOVBySZgGSfsRMk56t8JiGp0V9MWQOpGp0+DUllAWnh\npXZACugikErXvEByz5ACpJlVyB9SaZ9wJCSlPXXQzWRd6FyQ1CZIpb2e9YWShWStwKUg6den\nP6SVb2eZgmQcGWeG9Dq6LwVpOiA5l7wZkirXQlIbIVknekFq5wOSX0Cy59Wm5yGtGv/0kIwb\ntIkZgNR0MkjlWkjzVwqQjIv7QapGswIp9CJxhnBB0q+r1CEpUUjOzU0Q0mjnZgNpdh4gTS95\nsQlI9l2a8eWkIBlXMJBiBSR73mEaSJEhjT68CkgCF4kzRFqQysl/iceXm4HknD0TSLojIC2W\nMKRSZQVpdL4XpO6kaJBmZgNSF5Cml7yYE5K9v4+AVNpzV91/QPIISPa8w3SakMa3Z9OzJw9p\nvKzxR6TXPycPSV0RkirXQFq4ToLu2tkzOS7nuoUZnTN/4tUgVauvlQgByZq3/yEepPFMrpOA\nNKzG4lq0kI5zdD1I7ZedIfVfI0Fy/xmEESRtrVOFZK1m8+PiWigg+QYk89QcIbnmtdez/glI\n8To9JPM5A/0cILlXA0g+eULqfgaSvfR4kNQ2SJUCUsBF4gwxBak0zh9PXxmSMVMukIw/wXRE\nQLLmHc0SlgXJvacPgFQaMw0jxoSk3RMA0roShzS8vXUaktB1UpmEJg8gxwmbILl1qc2QzPt2\naUBasRZpQFr4HA8gBRQB0upbNQckx00xkES6OKTRE3rjOcKSh7T+7qF2BzEepMX7NNsgqeZf\nCiB5XyTOENeBNLVcN6TSmEefNxokVQ2QpmYHUvhF4gwBpMq8EJAiBaTxlDlHWFlDmnq6frw6\ngpDs90QBKW5AWjP6BKTSnEefNw1I1rNAQIpXECTX08CxIc0dcPtBajYTSOIBaTzlvohfESBt\nGX0nSHNzBUNatRaHQ6pXAEijmY6D1M+3O6RuZG3nrBh6E6T5Z7+BJHCROEOshFSOZjovpNLa\nuAwgrVgLIPkWBskxw0UgvSi5bpD2hDQ5O5DCLxJniLWQ7H+m5ara+1L+kPwduSFNDO0LSRtk\n/uzVkIx1AFLkzgqpOhukbsEDpOm5gRR+kThDjB5aO2dQpZJ628SoFtJwmDpnGs7KD5KaeD26\nfTaQti8VSH0XgDT1gnRzwT2k5fuBBqRVT9oBybuVQ4yfRhifD6RmAkgBAan9KvVSBrsrQNp0\n125h3hBIBzpqJc8GpJDWQuoPt2G+JQMrBt8J0sJKeEDauhJA8k0a0tF37YbDrb81koQ0uZTh\n9ApIAQHJ+CJfD8m4u2bPFA2SdoMzOXQ3BaSAgLQwQ2hVswbDEeKcSb9ndW1InisBJN+AtGZw\nIO0VkBZmCA1IQGoDUkirIDUHUCsISH6QDv01EpDUwgyhrYTU6dHnA9L6lQCSb0BaM/h2SPrx\nmAakVesAJN+AtGbwtCBN/81Ca14g+V8k0hCZQdK+7Q+p/9btjxiQ5pcIpOCLRBoCSP3k1CzW\n1HAQr3uV2+qV2AZp0AykqJ0QkqpckEKO5eQgLS0xa0hLT78DKSQgeUAy7l8CKWong9R+PSUk\nY8FbIa18nAYk3/KDpB/Wo7nar2eGpCogbQ1IfalAmlpO8pDWrcLhkBSQgGRMHQpp+GUWkDwv\nEmmIJUjLMwTWfuL1AqR+ZgUkayWAFLfzQtLv36jLQRqtBJDith7S/OYBaXwCkDwCUtz9DyQg\ntQEppAZS++Bn3UGRCKQycPB+gUBqAlJIAZD65x4CBk8L0vIStXnbtQBS3HKEtPKwBBKQ/C8S\naQggDdMTs4xPAJJHQLosJPfigeQXkIBknyoLSW2BNF6LDTsNSB5lCGn9QQSkzZDKCkhe5QPp\nufwASEGHsvE8oYvMAiQRR7tBOtQRkM4Mybg3OSbjXD6Q/AJSfEjde2oShOS8wxcR0tolZglp\nYQ4gBVUBSfsOpE0BacgDks+Rt7Ao15LmIYk91+AFqX8ODkgBfb0Vxce3yBBA0lbEXjEgCZYU\npKK+4HtRd5cYIilIay9xKKTuEE4E0toLHA6pXPw14d6Q7sX9odTfvfgSGOLqkCam25+d/4oC\nyav0IN2Kx2v6UbwJDJEjJL8jb3ZJ9nT786kgHfv72AQhFYX2Q+gQWUOauO/lsyQFpMilB+lf\nB+kmMMQKSJH3f/3gPQVI9qKAJFpikD4+v76L/56Tj/v8sw1A2rSk0Q9zkPq9BqT1JQapqZ68\nPQSGANLED5lAWvvsN5DMfn+/vj4+6qcc7rOOgLRtSaMf2uM6YUj1KuQEaWn8s7+yAUij02Uh\n6Utev8QKSGlBWtg8IDku0+0UIK0PSPEhbT0iK20KSOsC0vRCZH6PlCEk/cJAWheQphcCpNUf\n8zA7uPMHIAmXLiSRIdKA5H1AxoY09fR36bxEaEDaGpCGUoVUOU7rTgLS9nKCVOituwiQpn4C\nkmyJQfr5/KiZfNx/RIZYdlJeGpL7MkDaXlKQHm/aTc67yBCLTpKGFHoo+0KSGd2xZCBtyhfS\nvbj991tP/X3fRF60enFIMws7BNKWBVbbIMV+O8ziCqQE6Vb89tO/Im+jANLUwoAkW1KQjKcQ\nRH6PBKSphc1BijI6kLYvlFukoTBIogEpYklBej5G+v6rp3iMFCEgRSwpSN0ncdW9SbyxbwWk\nlQvybtNzVVE7N6RjHa040vb9PdK9/j3S7eNT5vdIQNICUszSgiQ+BJC0qonpqZmAtCEgRQ5I\nw+KAtK1gSMsvpQOSR0CKGJAiB6RhcZshrb5AApCWZgBSWGlCml4lIPkFpMjlBkk7C0gbAlLk\ngDQsDkjbApJWvpCkV3s7pNXPNQDJt9WQoq7FmoA0LG8TJFUCyWdF4gxx9O5NCtK6e21A8gpI\nsQv9cDrBgBQvIMUOSP0CNy2xAhKQ9IDULxBI2wKSXoqQ5tYISF4BKXahn6kl2NGQts0NJCDp\nAclvgUACklFCkPpDGUjiASl2CUKaXaMsIUX/7I3lFViaAUiBAclvgUACkhGQ/BYIpJQgJRCQ\n/BaYGaTFgBRYepDmVwhIcQJSaAlBatYFSEcEpNCA5LVAIAHJDEheCwQSkMySgrT89qh4kLYF\nJCCZpQTpRQlIhwSk0NKCtBiQ4gSki5UppIhrIhOQLhaQ4gSkiwWkOAHpYq15q8UePSFtWAUg\n+QWkaAEpTkC6WECKE5Cu1pqXiO9QteUhEpA8A1K8gBQlIF2tRCA979sBKXpAiheQogSkqwWk\nKAHpagEpSkC6WkCKEpCuFpCiBKSrBaQoAelqrfmooT3aBCn9gHS1gBQlIF0tIEUJSFcLSFEC\n0tUCUpSAdLWSgZTAOggGpKsFpCgB6WoBKUpAulpAihKQrhaQogSkqwWkKAHpagEpSkC6Wiv+\n9MsuAQlIWQekKAHpagEpSkC6WkCKEpCuVjKQElgHwYB0tYAUJSBdrVQgJbEOcgHpagEpSkC6\nWpVK5BhOYiXEAtLlqhI5hpNYCbGAdLmAFCMgXS4gxQhIlyuV34SmsRZSAelyASlGQLpcQIpR\nopAoXtXzfymUxlqI5XGUy8M5vlNuVNeZNy7jbct41ac75UZ1nXnjMt62jFd9ulNuVNeZNy7j\nbct41ac75UZ1nXnjMt62jFd9ulNuVNeZNy7jbct41ac75UZ1nXnjMt62jFd9ulNuVNeZNy7j\nbct41ac75UZ1nXnjMt62jFd9ulNuVNeZNy7jbct41ac75UZ1nXnjMt62jFd9ulNuVNeZNy7j\nbct41ac75UZ1nXnjMt62jFedKJ2ARCQQkIgEAhKRQEAiEghIRAIBiUggIBEJBCQigYBEJBCQ\niAQCEpFAQCISCEhEAgGJSCAgEQmUP6Svt+J2f9ST95tj0vtj0VPIvXHP07vtMU7Nq6Vty+uK\ny2U9J7vXe/v2uhbe68k3ZUz+5nV9mLk3rt6oZsI4Na+Wti2zKy6X9Zzqt/j3eP0j9k+pn+L2\nq35vxY8x+Vt8HL2O3rk3Tr2+N9ebcWpeLW5bZldc7pA+mg147fx78f2c+q/4NCa/Xl8yzb1x\nz016bw82/dTMWty2zK643CG1vXb+R/Gn2n/ItMmv4uvolQvN2jhV3FV7sOmn5tn0tmV2xZ0D\n0qN4V90V8PqmTX4U3/+ej2SPXLvA7I1Tv+aP/bcMm9m2zK64bK8Co6/XnYMpSHXvR65eWPbG\nad+zhzSzbZldcdleBXp/t/pegRNSUfz3/Ifvntf9BL3RxqnRj9lCmt+2rK64XK8Cvcet/mfL\nDamdJc+niJVr48Y/5gppdtvaWXK54jK9Cozem319G66P2+gAy/VYc2yc9n28nVk1u23K9VO6\nZbKaM/29vf/VE82TP3/Ds3Z/2rNZuVwfVq6Ne2U8a/eX57N2C9umXD+lWyarOd13/3D0s/51\nxHdxNyZvxet355kea86Ne9UeXtapWbW0bZldcblD+hue1nG/suH+un4eze/8csu9ca/yf2XD\n4rZldsXlDulfMbwk6214vnSYfNzqyRz/zZ7aODXc4XnL6ilivcVty+yKyx1SoV0fj/pFxPXJ\n1uRbJs+hWk1snBogmafm1Lpty+eKyx0SURIBiUggIBEJBCQigYBEJBCQiAQCEpFAQCISCEhE\nAgGJSCAgEQkEJCKBgEQkEJCIBAISkUBAIhIISEQCAYlIICARCQQkIoGARCQQkIgEAhKRQEAi\nEghIRAIBiUggIBEJBCQigYBEJBCQiAQCEpFAQCISCEhEAgFp35x/pHvmL3d/e/8t4nqh3R9g\n/bb+vvvjX1HcP5pzPzL5K61pB6R92wjpr/7T3t4jvRXjxdSDfRRF8fko/l4ntN8oKCAl0DSk\n97C/D9stWF9MfVpR47k3f//4nuMfc04tICXQJKT//G+Q9AUbi2khvSYfxX/aNwoJSPv2OoKf\nNwcfxe2z/vl+K+7tYf31Vtxef8T7vfh5fv0p/j3vmr03l+nn/37eJzP/ivnzUs2f/n4u5LOe\n6/58+NP83P3V8Lf2JqcbrP9z4u9v9entNwoISPvWQLq9DuSXjPfXxEf/sKUo3l8PaG7PH2+3\nxxNTS6Sb/7MhoEl67y71nKs+9/u9nWOA1C5mGKyH9FWb7b5RQEDatwbS++N58L697nPdftXv\n7XXi9+vEx3vx/TquP59k/nvdtvw2l+nmL16n/qfdE+wW8F8/V/P11o30mqldjDZYd5/vtzH5\nW4Q9FCMg7V1zeP+0Ux/11Hcz+Xoc8yhez1O/F1/t90dzmW7+YRltHy94L4TDXH9qQNTM2S5G\nG6xbxKO+Leu+UUBA2rfh8B6m2smiv8f1VwwelD7/86zvz3cNkrEAc177NONbtwjzLPKPPbhv\nqyA974zdu9OVweF9mEdZcwDp0NiD+zYDaZhp8hbpX/H29f0HpARjD+6beXg3D3F+hsmmj+dj\npNejlv4xknFJHVL3GOljDlL/GKkfjMdI4gFp30xI38MTafVzaqp+kuG/5x27z9dT1vfmaWkd\nx4/61R8jGc/a2fN2Tz20i/keP2v309yF/OFZu+CAtG/WHa76l0f/tIc/tz/1uNW/R3oa+Kl/\n16TNf28fRw3P4um/RzLnff3/rXg9Ed4uRh+shfTZEPvk90jBAWnf7Ecun8YrG4p/f68HQs0r\nG96HVzb0X58M3n/qe3Kdha/b8MoGZUP6eat/udu9smEYrL0wr2wQC0gp9y3zwuypxfw1j8v+\nCt5IERyQki7w1d8Li+HV33IBKekC3o+0vBjejyQYkNLu+1+8xfz71r9RUEAiEghIRAIBiUgg\nIBEJBCQigYBEJBCQiAQCEpFAQCISCEhEAgGJSCAgEQkEJCKBgEQkEJCIBAISkUBAIhIISEQC\nAYlIICARCQQkIoGARCQQkIgEAhKRQEAiEghIRAIBiUig/wEa98pK0GkHpAAAAABJRU5ErkJg\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(hp1$cycle, x=index(na.omit(df)), type='l', col='green')\n",
    "lines(r1$residuals, x=index(na.omit(df)), col='red')\n",
    "abline(0,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "nota-se que os desvios cíclicos são menores (mais próximos de zero) no procedimento HP Padrão\n",
    "\n",
    "**8 . Estime uma regressão da primeira diferença logarítimica de YIGD na tjr (e uma\n",
    "constante). Analise os resultados. A tjr parece afetar o produto industrial\n",
    "significativamente? **\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df$d_yigd = diff(log(df$YIGD))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = d_yigd ~ 1 + TJR, data = data.frame(df))\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.136664 -0.007871  0.002428  0.009475  0.058166 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)\n",
       "(Intercept)  0.004987   0.005273   0.946    0.346\n",
       "TJR         -0.002932   0.003382  -0.867    0.387\n",
       "\n",
       "Residual standard error: 0.01841 on 172 degrees of freedom\n",
       "  (2 observations deleted due to missingness)\n",
       "Multiple R-squared:  0.004351,\tAdjusted R-squared:  -0.001438 \n",
       "F-statistic: 0.7516 on 1 and 172 DF,  p-value: 0.3872\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm(d_yigd ~ 1 + TJR, data = data.frame(df)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "não parece haver relação estatisticamente significativa entre a primeira diferença logarítimica de YIGD e tjr."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** 9 . Estime agora a regressão da primeira diferença logarítimica de YIGD no ciclo da tjr\n",
    "estimado pelo método (a- tendência determinística). Compare os resultados aos\n",
    "obtidos no item anterior. **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = d_yigd ~ ciclo_a, data = data.frame(ciclo_a = residuals(r1), \n",
       "    na.omit(df$d_yigd)))\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.138103 -0.008212  0.001966  0.009649  0.058366 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)\n",
       "(Intercept)  0.0005361  0.0013850   0.387    0.699\n",
       "ciclo_a     -0.0043114  0.0034373  -1.254    0.211\n",
       "\n",
       "Residual standard error: 0.01832 on 173 degrees of freedom\n",
       "Multiple R-squared:  0.009012,\tAdjusted R-squared:  0.003284 \n",
       "F-statistic: 1.573 on 1 and 173 DF,  p-value: 0.2114\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm(d_yigd ~ ciclo_a, data=data.frame(ciclo_a=residuals(r1), na.omit(df$d_yigd))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Em linha com os resultados do item anterior, não parece haver significância estatística na relação entre a primeira diferença logarítimica de YIGD e o ciclo da tjr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** 10 . Estime agora a regressão da primeira diferença logarítimica de YIGD no ciclo da tjr\n",
    "estimado pelo método (c- filtro HP). Compare os resultados aos obtidos nos itens\n",
    "anteriores. **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = d_yigd ~ ciclo_c, data = data.frame(ciclo_c = hp1$cycle, \n",
       "    na.omit(df$d_yigd)))\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.136930 -0.007810  0.002201  0.009704  0.060039 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)\n",
       "(Intercept)  0.0005361  0.0013851   0.387    0.699\n",
       "ciclo_c     -0.0061135  0.0048975  -1.248    0.214\n",
       "\n",
       "Residual standard error: 0.01832 on 173 degrees of freedom\n",
       "Multiple R-squared:  0.008927,\tAdjusted R-squared:  0.003198 \n",
       "F-statistic: 1.558 on 1 and 173 DF,  p-value: 0.2136\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm(d_yigd ~ ciclo_c, data=data.frame(ciclo_c=hp1$cycle, na.omit(df$d_yigd))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mais uma vez, em linha com os resultados anteriores, não a evidência estatística de relação entre as variáveis.\n",
    "\n",
    "**11 . Aplique o filtro HP à série YIGD em logaritmo, usando o valor padrão de “lambda”. Em\n",
    "seguida, estime a regressão do ciclo de YIGD assim obtido no ciclo da tjr estimado pelo\n",
    "método (c- filtro HP). Compare os resultados aos obtidos nos itens anteriores**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = hp_d_yigd ~ 1 + ciclo_c, data = data)\n",
       "\n",
       "Residuals:\n",
       "      Min        1Q    Median        3Q       Max \n",
       "-0.136939 -0.007938  0.002354  0.009276  0.059629 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)\n",
       "(Intercept)  1.105e-18  1.361e-03   0.000    1.000\n",
       "ciclo_c     -4.824e-03  4.812e-03  -1.003    0.317\n",
       "\n",
       "Residual standard error: 0.018 on 173 degrees of freedom\n",
       "Multiple R-squared:  0.005776,\tAdjusted R-squared:  2.924e-05 \n",
       "F-statistic: 1.005 on 1 and 173 DF,  p-value: 0.3175\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data=data.frame(ciclo_c=hp1$cycle, hp_d_yigd=hpfilter(na.omit(df$d_yigd), freq=14400)$cycle)\n",
    "summary(lm(hp_d_yigd ~ 1 + ciclo_c, data=data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "nota se uma redução acentuada do erro padrão.\n",
    "\n",
    "**13 . Simule um processo ruído branco de tamanho 300 e analise sua FAC e FACP. Em\n",
    "seguida, aplique o filtro HP à série gerada e analise o par FAC/FACP do componente\n",
    "cíclico desta série. Compare com o par FAC/FACP da série original. Repita o\n",
    "procedimento algumas vezes. Os resultados obtidos sugerem alguma cautela no uso\n",
    "do filtro HP (e outros métodos de “suavização”)?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kR1Eak9EMm2GVFdPyLx+0hWIJJtM6K6bkRKN09mWkSkORDJthlRXS8iCWIgkpA4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\nEAnAAEQCMACRAAxAJAAD/gfDCIb9qXnvtQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Series  wn_hp\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wn = rnorm(300)\n",
    "wn_hp = hpfilter(wn, freq=1600)$cycle\n",
    "par(mfrow=c(2,2))\n",
    "acf(wn)\n",
    "pacf(wn)\n",
    "acf(wn_hp)\n",
    "pacf(wn_hp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Os resultados sugerem que o uso de métodos de suavização podem introduzir autocorrelação entre as variáveis."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}