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<h2 id="toc-title">Sumário</h2>
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<li><a href="#os-modelos-temporais-multivariados" id="toc-os-modelos-temporais-multivariados" class="nav-link active" data-scroll-target="#os-modelos-temporais-multivariados"><span class="toc-section-number">1</span> Os Modelos Temporais Multivariados</a></li>
<li><a href="#objetivo-e-ferramentas" id="toc-objetivo-e-ferramentas" class="nav-link" data-scroll-target="#objetivo-e-ferramentas"><span class="toc-section-number">2</span> Objetivo e Ferramentas</a></li>
<li><a href="#dados-brutos-e-tratamentos" id="toc-dados-brutos-e-tratamentos" class="nav-link" data-scroll-target="#dados-brutos-e-tratamentos"><span class="toc-section-number">3</span> Dados Brutos e Tratamentos</a></li>
<li><a href="#raíz-unitária-com-kpss-e-pp" id="toc-raíz-unitária-com-kpss-e-pp" class="nav-link" data-scroll-target="#raíz-unitária-com-kpss-e-pp"><span class="toc-section-number">4</span> Raíz Unitária com KPSS e PP</a></li>
<li><a href="#funções-de-autocorrelações" id="toc-funções-de-autocorrelações" class="nav-link" data-scroll-target="#funções-de-autocorrelações"><span class="toc-section-number">5</span> Funções de Autocorrelações</a></li>
<li><a href="#var" id="toc-var" class="nav-link" data-scroll-target="#var"><span class="toc-section-number">6</span> VAR</a>
<ul class="collapse">
<li><a href="#var_1-petro-us-câmbio-e-ipca" id="toc-var_1-petro-us-câmbio-e-ipca" class="nav-link" data-scroll-target="#var_1-petro-us-câmbio-e-ipca"><span class="toc-section-number">6.1</span> <span class="math inline">VAR_{1}</span>: Petro US$, Câmbio e IPCA</a></li>
<li><a href="#var_2-petro-r-e-ipca" id="toc-var_2-petro-r-e-ipca" class="nav-link" data-scroll-target="#var_2-petro-r-e-ipca"><span class="toc-section-number">6.2</span> <span class="math inline">VAR_{2}</span>: Petro R$ e IPCA</a></li>
</ul></li>
<li><a href="#diagnóstico-dos-resíduos-do-var" id="toc-diagnóstico-dos-resíduos-do-var" class="nav-link" data-scroll-target="#diagnóstico-dos-resíduos-do-var"><span class="toc-section-number">7</span> Diagnóstico dos Resíduos do VAR</a>
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<li><a href="#autocorrelação-breusch-godfrey" id="toc-autocorrelação-breusch-godfrey" class="nav-link" data-scroll-target="#autocorrelação-breusch-godfrey"><span class="toc-section-number">7.1</span> Autocorrelação: Breusch-Godfrey</a></li>
<li><a href="#autocorrelação-ljung-box" id="toc-autocorrelação-ljung-box" class="nav-link" data-scroll-target="#autocorrelação-ljung-box"><span class="toc-section-number">7.2</span> Autocorrelação: Ljung-Box</a></li>
<li><a href="#autocorrelação-fac-e-facp-nos-resíduos" id="toc-autocorrelação-fac-e-facp-nos-resíduos" class="nav-link" data-scroll-target="#autocorrelação-fac-e-facp-nos-resíduos"><span class="toc-section-number">7.3</span> Autocorrelação: FAC e FACP nos Resíduos</a></li>
<li><a href="#heterocedasticidade-arch-multiplicador-de-lagrange" id="toc-heterocedasticidade-arch-multiplicador-de-lagrange" class="nav-link" data-scroll-target="#heterocedasticidade-arch-multiplicador-de-lagrange"><span class="toc-section-number">7.4</span> Heterocedasticidade: ARCH Multiplicador de Lagrange</a></li>
<li><a href="#quebra-estrutural-teste-cusum" id="toc-quebra-estrutural-teste-cusum" class="nav-link" data-scroll-target="#quebra-estrutural-teste-cusum"><span class="toc-section-number">7.5</span> Quebra Estrutural: Teste CUSUM</a></li>
</ul></li>
<li><a href="#teste-de-cointegração-de-johansen" id="toc-teste-de-cointegração-de-johansen" class="nav-link" data-scroll-target="#teste-de-cointegração-de-johansen"><span class="toc-section-number">8</span> Teste de Cointegração de Johansen</a></li>
<li><a href="#vecm-do-trio-de-variáveis" id="toc-vecm-do-trio-de-variáveis" class="nav-link" data-scroll-target="#vecm-do-trio-de-variáveis"><span class="toc-section-number">9</span> VECM do Trio de Variáveis</a></li>
<li><a href="#formas-estruturais" id="toc-formas-estruturais" class="nav-link" data-scroll-target="#formas-estruturais"><span class="toc-section-number">10</span> Formas Estruturais</a></li>
<li><a href="#função-impulso-resposta" id="toc-função-impulso-resposta" class="nav-link" data-scroll-target="#função-impulso-resposta"><span class="toc-section-number">11</span> Função Impulso-resposta</a></li>
<li><a href="#decomposição-da-variância-do-erro" id="toc-decomposição-da-variância-do-erro" class="nav-link" data-scroll-target="#decomposição-da-variância-do-erro"><span class="toc-section-number">12</span> Decomposição da Variância do Erro</a></li>
<li><a href="#decomposição-histórica" id="toc-decomposição-histórica" class="nav-link" data-scroll-target="#decomposição-histórica"><span class="toc-section-number">13</span> Decomposição Histórica</a></li>
<li><a href="#outras-referências" id="toc-outras-referências" class="nav-link" data-scroll-target="#outras-referências"><span class="toc-section-number">14</span> Outras Referências</a></li>
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<div class="quarto-title-block"><div><h1 class="title">VAR e VECM no R: Como o preço internacional do petróleo afeta os preços domésticos?</h1><button type="button" class="btn code-tools-button dropdown-toggle" id="quarto-code-tools-menu" data-bs-toggle="dropdown" aria-expanded="false"><i class="bi"></i> Code</button><ul class="dropdown-menu dropdown-menu-end" aria-labelelledby="quarto-code-tools-menu"><li><a id="quarto-show-all-code" class="dropdown-item" href="javascript:void(0)" role="button">Show All Code</a></li><li><a id="quarto-hide-all-code" class="dropdown-item" href="javascript:void(0)" role="button">Hide All Code</a></li><li><hr class="dropdown-divider"></li><li><a id="quarto-view-source" class="dropdown-item" href="javascript:void(0)" role="button">View Source</a></li></ul></div></div>
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<div class="quarto-title-meta-heading">Author</div>
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<p>Heitor Gabriel Monteiro </p>
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<p class="date">February 22, 2023</p>
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<section id="os-modelos-temporais-multivariados" class="level1" data-number="1">
<h1 data-number="1"><span class="header-section-number">1</span> Os Modelos Temporais Multivariados</h1>
<p>Faz parte de todo grande projeto econômico saber de que forma alguns fatores podem influenciar sua variável de interesse. Por exemplo, como o preço da concorrência afeta na demanda de uma empresa? Como juros mais altos impactam no perfil de demanda por crédito? Uma excelente ferramenta teórica para trabalhar com essas relações empíricas de pressupostos teóricos, num contexto de séries de tempo, é a Análise Autorregressiva Vetorial Multivariada, com seus principais modelos sendo o VAR (Vetor Autorregressivo) e o VECM (Modelo Vetorial de Correção de Erros).</p>
<p>Diferentemente do <a href="https://heitorgabriel.github.io/time-series-modelling_1/">caso autorregressivo univariado (<span class="math inline">AR(p)</span>),</a> o VAR regride um conjunto de variáveis, explicando-as com suas próprias realizações passadas e, por ser um sistema, com os valores atuais e passados das demais variáveis do conjunto. Tomando como exemplo um caso bivariado de ordem 1 <span class="math inline">(p=1)</span>:</p>
<p><span class="math display">
\begin{Bmatrix}
y_{t} = b_{10} + a_{12}z_{t} + b_{11}z_{t-1} + b_{12}y_{t-1} + \sigma_{y}\epsilon_{y,t} \\
z_{t} = b_{20} + a_{22}y_{t} + b_{21}z_{t-1} + b_{22}y_{t-1} + \sigma_{z}\epsilon_{z,t}
\end{Bmatrix}
</span></p>
<p><span class="math display">
\begin{Bmatrix}
-a_{12}z_{t} + y_{t} = b_{10} + b_{11}z_{t-1} + b_{12}y_{t-1} + \sigma_{y}\epsilon_{y,t} \\
+z_{t} - a_{22}y_{t} = b_{20} + b_{21}z_{t-1} + b_{22}y_{t-1} + \sigma_{z}\epsilon_{z,t}
\end{Bmatrix}
</span></p>
<p><span class="math display">
\begin{bmatrix}
-a_{12} & 1 \\
1 & -a_{22}
\end{bmatrix}
\begin{bmatrix}
z_{t} \\ y_{t}
\end{bmatrix}
=
\begin{bmatrix}
b_{10} \\ b_{20}
\end{bmatrix}
+
\begin{bmatrix}
b_{11} & b_{12} \\
b_{21} & b_{22}
\end{bmatrix}
\begin{bmatrix}
z_{t-1} \\ y_{t-1}
\end{bmatrix}
+
\begin{bmatrix}
\sigma_{z} & 0 \\
0 & \sigma_{y}
\end{bmatrix}
\begin{bmatrix}
\epsilon_{z,t} \\ \epsilon_{y,t}
\end{bmatrix}
</span><br>
Dando nomes às matrizes formadas, respectivamente:</p>
<p><span class="math display">
AX_{t} = B_{0} + B_{1}X_{t-1} + B_{\sigma}\epsilon_{t}
</span></p>
<p>Nesse formato, chamado <em>estrutural</em>, assumimos que <span class="math inline">(y_t, z_t)</span> são estacionárias; que a sequência de erros são ruídos brancos, não-correlacionados entre si e com <span class="math inline">(\sigma_{y}, \sigma_{z})</span> sendo seus desvios-padrão. O problema é que essa forma não pode ser estimada diretamente via MQO porque uma variável tem efeito contemporâneo na outra (efeito feedback), ou seja, <span class="math inline">(z_{t}, y_{t})</span> é afetado por <span class="math inline">(\epsilon_{y,t}, \epsilon_{z,t})</span>, respectivamente. Ainda estamos interessados nos choques estruturais, mas, para a estimação, devemos calculá-lo no <em>formato reduzido</em>:</p>
<p><span class="math display">
X_{t} = A^{-1}B_{0} + A^{-1}B_{1}X_{t-1} + A^{-1}B_{\sigma}\epsilon_{t}
</span></p>
<p>Com <span class="math inline">\Phi_{0} = A^{-1}B_{0}</span>, <span class="math inline">\Phi_{1} = A^{-1}B_{1}</span> e <span class="math inline">e_{t} = A^{-1}B_{\sigma}\epsilon_{t}</span> temos:</p>
<p><span class="math display">
X_{t} = \Phi_{0} + \Phi_{1} X_{t-1} + e_{t}
</span></p>
<p>Nesse formato, os erros transformados não são mais correlacionados aos regressores, permanecem não-autocorrelacionados, mas são correlacionados contemporâneamente entre si:</p>
<p><span class="math display">
\begin{bmatrix}
e_{1,t} \\ e_{2,t}
\end{bmatrix}
\equiv
A^{-1}B_{\sigma}\epsilon_{t}
=
\begin{bmatrix}
\frac{\sigma_{y}\epsilon_{y,t} - a_{12}\sigma_{z}\epsilon_{z,t}}{1 - a_{12}a_{21}}
\\
\frac{\sigma_{z}\epsilon_{z,t} - a_{21}\sigma_{y}\epsilon_{y,t}}{1 - a_{12}a_{21}}
\end{bmatrix}
</span></p>
<p>Estabelecer restrições à forma reduzida para voltar aos choques estruturais é o cerne da modelagem VAR e VECM.</p>
<p>Os modelos VECM podem ser descritos como a consideração de que as variáveis não-estacionárias têm uma relação estável, ou seja, alguma transformação linear entre elas que seja estacionária. Nesse comportamento, há uma correção de desvios dessa relação, no curto-prazo. De forma bem sucinta, o caso na forma reduzida, bivariado e de ordem 2 é:</p>
<p><span class="math display">
\begin{Bmatrix}
\Delta y_{t} = b_{10} + a_{12}( \alpha + y_{t-1} + \beta z_{t-1}) + b_{11}\Delta z_{t-1} + b_{12}\Delta y_{t-1} + u_{y,t} \\
\Delta z_{t} = b_{20} - a_{22}( \alpha + y_{t-1} + \beta z_{t-1}) + b_{21}\Delta z_{t-1} + b_{22}\Delta y_{t-1} + u_{z,t}
\end{Bmatrix}
</span> Onde <span class="math inline">(a_{12},a_{22})</span> é a velocidade de ajuste dos desvios da relação estacionária de longo-prazo <span class="math inline">\alpha + y_{t-1} + \beta z_{t-1}</span>. Para testar cointegração das variáveis, procedemos com o Teste de Johansen.</p>
<p>Com as restrições que impormos ao modelo, podemos chegar à sua forma estrutural e realizar análises impulso-resposta e decomposição da variância. A função impulso-resposta mostra o impacto de um choque de <span class="math inline">\epsilon_{z,t}</span> em <span class="math inline">z_{t+h}</span>, com <span class="math inline">h=(1,2,...)</span>. E a decomposição da variância diz qual que porcentagem da variância do erro de previsão decorre de cada variável endógena, ao longo do horizonte de previsão.</p>
</section>
<section id="objetivo-e-ferramentas" class="level1" data-number="2">
<h1 data-number="2"><span class="header-section-number">2</span> Objetivo e Ferramentas</h1>
<p>Nesse exercício, vamos calcular as relações entre:</p>
<ol type="1">
<li>preço internacional do petróleo;</li>
<li>câmbio e</li>
<li>índice nacional de preços</li>
</ol>
<p>para responder à pergunta: <strong>Qual impacto do aumento do preço internacional do petróleo nos preços domésticos?</strong> A ideia é que o preço no mercado internacional do petróleo tem poder suficiente para afetar não somente o preço doméstico dos combustíveis, portanto, dos transportes, mas também de todas cadeias produtivas que usam a energia fóssil, como o gás de cozinha (GLP) para alimentação. O preço internacional do petróleo pode afetar a economia local através do seu valor convertido para o Real, que é o valor que os agentes olharão para decidir suas alocações de insumos e produção. Uma ideia <em>a priori</em> é que os nossos preços e o câmbio não têm capacidade de influenciar o preço internacional do petróleo, parece ser bem razoável e o testaremos com Granger-causalidade e pela significância dos coeficientes. Também é provável que a política nacional de atualização de preços dos combustíveis possa <em>sujar</em> essa relação que estimaremos. Outro pessuporto que precisamos adotar, portanto, é que, ao olhar para o preço internacional do petróleo, os agentes preverão uma variação do preço doméstico, que acontecerá cedo ou tarde, e anteciparão a atualização. Portanto, de forma mais técnica, o que testaremos é o efeito, nos preços domésticos, da influência esperada do preço internacional do petróleo.</p>
<p>Vamos conhecer o comportamento dessas variáveis; calcular modelos VAR; diagnosticar os resíduos para examinar a qualidade dessas relações; testar cointegração, para ver se é necessário usar um VECM como alternativa; modelar a versão Estrutural do VAR ou do VECM e usar algumas firulas do instrumental: o Impulso-Resposta e a Decomposição da Variância. Uma análise subsequente ao VECM seria o de assimetria no vetor de correção de erros: as respostas a desvios positivos são mais rápidas que as respostas a desvios negativos, simularemos também essa restrição.</p>
<p>Usaremos os sequintes pacotes do R:</p>
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<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse) <span class="co"># manipulação e visualizações básicas</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(plotly) <span class="co"># visualizações interativas</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggpubr) <span class="co"># diversidade de configurações de visualização</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(kableExtra) <span class="co"># tabelas</span></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="co"># tidyverts core: pacotes para séries temporais univariadas</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tsibble)</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(fable)</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(feasts)</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="co"># tidyverts improvements tools</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tsibbletalk)</span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(fable.prophet)</span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(fabletools)</span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a><span class="co"># Multivariáveis: pacotes para séries temporais multivariadas</span></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(vars)</span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tsDyn)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
</div>
<p>Recomendo fortemente passear pela documentação do conjunto de pacotes <a href="https://tidyverts.org/">Tidyverts</a>, ler as definições na documentação do <a href="https://www.pfaffikus.de/rpacks/vars/files/vignette-vars.pdf">vars</a>, do <a href="https://rdrr.io/cran/tsDyn/f/inst/doc/ThCointOverview.pdf">tsDyn</a> e do <a href="https://www.jstatsoft.org/article/view/v097i05">svar</a>.</p>
</section>
<section id="dados-brutos-e-tratamentos" class="level1" data-number="3">
<h1 data-number="3"><span class="header-section-number">3</span> Dados Brutos e Tratamentos</h1>
<p>Para o preço internacional do petróleo, usaremos a média simples dos preços médios mensais, em dólar, dos três principais mercados da commodity: Dated Brent, Dubai Fateh e West Texas Intermediate. Para a taxa de câmbio, usaremos a taxa (R$ / US$) comercial de compra média para o mês. E para os preços nacionais, usaremos o índice histórico do IPCA (Tabela 1737).</p>
<p>Para facilitar a criação de tabelas, criaremos uma função:</p>
<div class="cell">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>set_tab <span class="ot"><-</span> <span class="cf">function</span>(dados_tab, cap_tab){</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">kable</span>( <span class="at">x =</span> dados_tab,</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a> <span class="at">booktabs =</span> <span class="cn">TRUE</span>,</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> <span class="at">escape =</span> <span class="cn">FALSE</span>,</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> <span class="at">digits =</span> <span class="dv">4</span>,</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> <span class="at">caption =</span> cap_tab) <span class="sc">|></span> </span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">kable_styling</span>(<span class="at">latex_options =</span></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">c</span>(<span class="st">"striped"</span>, <span class="st">"hold_position"</span>),</span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="at">position =</span> <span class="st">"center"</span>,</span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> <span class="at">full_width =</span> F,</span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> <span class="at">bootstrap_options =</span></span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">c</span>(<span class="st">"striped"</span>, <span class="st">"hover"</span>, <span class="st">"condensed"</span>, <span class="st">"responsive"</span>))</span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a>} </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
</div>
<p>Vamos importar os dados e fazer uns tratmentos:</p>
<div class="cell">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>dds <span class="ot"><-</span> <span class="fu">read_csv</span>(<span class="st">"dds.csv"</span>)</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>dds <span class="sc">|></span> <span class="fu">glimpse</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output cell-output-stdout">
<pre><code>Rows: 391
Columns: 7
$ date <chr> "1990M1", "1990M2", "1990M3", "1990M4", "1990M5", "1990M6"…
$ petro <dbl> 20.42522, 19.38833, 18.10379, 16.36810, 16.34986, 15.09730…
$ petro_brent <dbl> 20.98913, 19.70250, 18.46591, 16.92619, 16.67174, 15.55238…
$ petro_dubai <dbl> 17.50174, 16.68150, 15.75591, 14.25048, 14.64783, 13.27714…
$ petro_texas <dbl> 22.78478, 21.78100, 20.08955, 17.92762, 17.73000, 16.46238…
$ cambio <chr> "0,000005", "0,000009", "0,000013", "0,000017", "0,000019"…
$ ipca <dbl> 0.0054, 0.0095, 0.0173, 0.0200, 0.0216, 0.0241, 0.0272, 0.…</code></pre>
</div>
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Retirar NA's</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>dds <span class="ot"><-</span> dds <span class="sc">|></span> <span class="fu">filter</span>(<span class="sc">!</span><span class="fu">is.na</span>(petro)) </span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Substituir vírgula por ponto e reconhecer a variável numérica</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>dds<span class="sc">$</span>cambio <span class="ot"><-</span> dds<span class="sc">$</span>cambio <span class="sc">|></span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">str_replace</span>(<span class="at">pattern =</span> <span class="st">","</span>, <span class="at">replacement =</span> <span class="st">"."</span>) <span class="sc">|></span></span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">as.numeric</span>() </span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a><span class="co"># Criar uma variável de tempo chamada "dt" na base</span></span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a>dds<span class="sc">$</span>dt <span class="ot"><-</span> <span class="fu">seq</span>(<span class="at">from =</span> lubridate<span class="sc">::</span><span class="fu">ym</span>(<span class="st">'1990 Jan'</span>),</span>
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a> <span class="at">to =</span> lubridate<span class="sc">::</span><span class="fu">ym</span>(<span class="st">'2022 Jul'</span>), <span class="co"># alternativa: length=</span></span>
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a> <span class="at">by =</span> <span class="st">"month"</span>)</span>
<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a><span class="co"># Criar os logaritmos naturais</span></span>
<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a>dds <span class="ot"><-</span> dds <span class="sc">|></span> <span class="fu">mutate</span>(<span class="st">"ptr_br_log"</span> <span class="ot">=</span> <span class="fu">log</span>(cambio) <span class="sc">+</span> <span class="fu">log</span>(petro),</span>
<span id="cb5-16"><a href="#cb5-16" aria-hidden="true" tabindex="-1"></a> <span class="st">"ipca_log"</span> <span class="ot">=</span> <span class="fu">log</span>(ipca),</span>
<span id="cb5-17"><a href="#cb5-17" aria-hidden="true" tabindex="-1"></a> <span class="st">"petro_log"</span> <span class="ot">=</span> <span class="fu">log</span>(petro),</span>
<span id="cb5-18"><a href="#cb5-18" aria-hidden="true" tabindex="-1"></a> <span class="st">"cambio_log"</span> <span class="ot">=</span> <span class="fu">log</span>(cambio),</span>
<span id="cb5-19"><a href="#cb5-19" aria-hidden="true" tabindex="-1"></a> <span class="st">"petro_brent_log"</span> <span class="ot">=</span> <span class="fu">log</span>(petro_brent),</span>
<span id="cb5-20"><a href="#cb5-20" aria-hidden="true" tabindex="-1"></a> <span class="st">"petro_dubai_log"</span> <span class="ot">=</span> <span class="fu">log</span>(petro_dubai),</span>
<span id="cb5-21"><a href="#cb5-21" aria-hidden="true" tabindex="-1"></a> <span class="st">"petro_texas_log"</span> <span class="ot">=</span> <span class="fu">log</span>(petro_texas))</span>
<span id="cb5-22"><a href="#cb5-22" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-23"><a href="#cb5-23" aria-hidden="true" tabindex="-1"></a>dds <span class="sc">|></span> <span class="fu">glimpse</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output cell-output-stdout">
<pre><code>Rows: 391
Columns: 15
$ date <chr> "1990M1", "1990M2", "1990M3", "1990M4", "1990M5", "199…
$ petro <dbl> 20.42522, 19.38833, 18.10379, 16.36810, 16.34986, 15.0…
$ petro_brent <dbl> 20.98913, 19.70250, 18.46591, 16.92619, 16.67174, 15.5…
$ petro_dubai <dbl> 17.50174, 16.68150, 15.75591, 14.25048, 14.64783, 13.2…
$ petro_texas <dbl> 22.78478, 21.78100, 20.08955, 17.92762, 17.73000, 16.4…
$ cambio <dbl> 0.000005, 0.000009, 0.000013, 0.000017, 0.000019, 0.00…
$ ipca <dbl> 0.0054, 0.0095, 0.0173, 0.0200, 0.0216, 0.0241, 0.0272…
$ dt <date> 1990-01-01, 1990-02-01, 1990-03-01, 1990-04-01, 1990-…
$ ptr_br_log <dbl> -9.189302, -8.653614, -8.354440, -8.186963, -8.076853,…
$ ipca_log <dbl> -5.2213563, -4.6564635, -4.0570488, -3.9120230, -3.835…
$ petro_log <dbl> 3.016770, 2.964672, 2.896121, 2.795334, 2.794219, 2.71…
$ cambio_log <dbl> -12.206073, -11.618286, -11.250561, -10.982297, -10.87…
$ petro_brent_log <dbl> 3.044005, 2.980746, 2.915926, 2.828862, 2.813715, 2.74…
$ petro_dubai_log <dbl> 2.862300, 2.814300, 2.757215, 2.656790, 2.684292, 2.58…
$ petro_texas_log <dbl> 3.126093, 3.081038, 3.000200, 2.886342, 2.875258, 2.80…</code></pre>
</div>
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Permanecer somente com a data Julho de 1994 pra lá...</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>dds <span class="ot"><-</span> dds <span class="sc">|></span> <span class="fu">filter</span>(dt <span class="sc">>=</span> lubridate<span class="sc">::</span><span class="fu">ym</span>(<span class="st">"1994 Jul"</span>))</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Criar uma base tsibble</span></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>dd <span class="ot"><-</span> dds <span class="sc">|></span></span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">select</span>(dt, ptr_br_log, ipca_log, cambio_log, petro_log) <span class="sc">|></span> </span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">mutate</span>(<span class="at">dt =</span> tsibble<span class="sc">::</span><span class="fu">yearmonth</span>(<span class="fu">as.character</span>(dt))) <span class="sc">|></span></span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">as_tsibble</span>(<span class="at">index =</span> dt)</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a><span class="co"># Verificar o intervalo do tsibble</span></span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> <span class="fu">interval</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output cell-output-stdout">
<pre><code><interval[1]>
[1] 1M</code></pre>
</div>
</div>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>plt_cambio <span class="ot"><-</span> <span class="fu">plot_ly</span>(dds,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span>dt, <span class="at">y =</span> <span class="sc">~</span>cambio,</span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Câmbio"</span>,</span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#30d5c8"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'Taxa de Câmbio - R$/US$ - Comercial - Compra - Média - R$ '</span>,</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">"R$/US$"</span>,</span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb9-17"><a href="#cb9-17" aria-hidden="true" tabindex="-1"></a>plt_cambio</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div class="plotly html-widget html-fill-item-overflow-hidden html-fill-item" id="htmlwidget-0af577fa34c6363c7451" style="width:100%;height:505px;"></div>
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</div>
</div>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>plt_ipca <span class="ot"><-</span> <span class="fu">plot_ly</span>(dds,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span>dt, <span class="at">y =</span> <span class="sc">~</span>ipca,</span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"IPCA"</span>,</span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#551a8b"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'índice de Preços ao Consumidor Amplo - IPCA, Brasil, de Jan/90 a Jul/2022.'</span>,</span>
<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb10-9"><a href="#cb10-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb10-10"><a href="#cb10-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb10-11"><a href="#cb10-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb10-12"><a href="#cb10-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">"Índice"</span>,</span>
<span id="cb10-13"><a href="#cb10-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb10-14"><a href="#cb10-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb10-15"><a href="#cb10-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb10-16"><a href="#cb10-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb10-17"><a href="#cb10-17" aria-hidden="true" tabindex="-1"></a>plt_ipca</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
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<summary>Code</summary>
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>plt_petro <span class="ot"><-</span> <span class="fu">plot_ly</span>(dds,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span>dt, <span class="at">y =</span> <span class="sc">~</span>petro,</span>
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Petroleum"</span>,</span>
<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#2E8B57"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'Média do Preço Internacional do Petróleo'</span>,</span>
<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb11-8"><a href="#cb11-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb11-9"><a href="#cb11-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb11-10"><a href="#cb11-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb11-11"><a href="#cb11-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb11-12"><a href="#cb11-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">"Preço em Dólar"</span>,</span>
<span id="cb11-13"><a href="#cb11-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb11-14"><a href="#cb11-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb11-15"><a href="#cb11-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb11-16"><a href="#cb11-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb11-17"><a href="#cb11-17" aria-hidden="true" tabindex="-1"></a>plt_petro</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
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</div>
<p>Vamos também considerar o <strong>preço nacional do petróleo</strong>, que é o preço no mercado internacional convertido em reais pela taxa de câmbio apresentada:</p>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>plt_petro_n <span class="ot"><-</span> <span class="fu">plot_ly</span>(dds,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span>dt, <span class="at">y =</span> <span class="sc">~</span>petro<span class="sc">*</span>cambio,</span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Petroleum (R$)"</span>,</span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#073320"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'Média do Preço Internacional do Petróleo, em Reais'</span>,</span>
<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb12-10"><a href="#cb12-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb12-11"><a href="#cb12-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb12-12"><a href="#cb12-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">"Preço em Reais"</span>,</span>
<span id="cb12-13"><a href="#cb12-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb12-14"><a href="#cb12-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb12-15"><a href="#cb12-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb12-16"><a href="#cb12-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb12-17"><a href="#cb12-17" aria-hidden="true" tabindex="-1"></a>plt_petro_n</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
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<p>Conseguimos visualizar o regime brasileiro de câmbio fixo até o fim de 1998. O rápido crescimento do preço do petróleo em 2007 ocorreu por aumento da demanda mundial e estagnação da produção, enquanto que a queda observada a partir de julho de 2008 foi causada pela crise financeira na bolha imobiliária dos EUA<a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a>. A queda do preço internacional na metade de 2014 foi causada pela rápida expansão na produção norte-americana e mudanças na política de preços da OPEC<a href="#fn2" class="footnote-ref" id="fnref2" role="doc-noteref"><sup>2</sup></a>. Percebemos também a mudança na tendência dos preços do petróleo e do IPCA a partir de abril de 2020, momento que a COVID-19 já se tornara pandêmica.</p>
<p>A fins didáticos, faremos uma decomposição multiplicativa do logaritmo preço nacional do petróleo, é possível perceber melhor a tendência, a sazonalidade e os choques:</p>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> </span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">select</span>(ptr_br_log, dt) <span class="sc">|></span></span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">model</span>(<span class="fu">classical_decomposition</span>(</span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a> ptr_br_log,</span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"multiplicative"</span>)) <span class="sc">|></span></span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">components</span>() <span class="sc">|></span></span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">autoplot</span>() <span class="sc">|></span> </span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">plotly_build</span>() <span class="sc">|></span> </span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">title =</span> htmltools<span class="sc">::</span><span class="fu">HTML</span>(<span class="st">"Decomposição Multiplicativa Clássica:</span><span class="sc">\n</span><span class="st">petro_br_log = trend * seasonal * randon"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
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</div>
</section>
<section id="raíz-unitária-com-kpss-e-pp" class="level1 tabset tabset-fade tabset-pills" data-number="4">
<h1 class="tabset tabset-fade tabset-pills" data-number="4"><span class="header-section-number">4</span> Raíz Unitária com KPSS e PP</h1>
<p>Visualmente, percebemos tendência temporal no IPCA e um passeio aleatório nas demais variáveis, Petro e Câmbio. Faremos o teste de raíz unitária de Phillips-Perron e estacionaridade ao entorno de uma tendência de Kwiatkowski-Phillips-Schmidt-Shin (KPSS) para validar nossa intuição visual. Resumidamente, as raízes do polinômio real de operadores de defasagem devem estar dentro do ciclo unitário para que o processo <span class="math inline">AR(.)</span> seja estacionário e para que o processo <span class="math inline">MA(.)</span> seja invertível. Caso seja detectado raíz fora do ciclo, teremos que remover a tendência, diferenciando a série. Usaremos o teste PP para raíz unitária por ser robusto, se comparado a Dickey-Fuller (DF) na presença de tendência temporal, intercepto e correlação serial nos erros e o teste KPSS para estacionariedade pelo baixo poder do DF na presença de médias móveis perto do círculo unitário.</p>
<p>A hipótese nula do KPSS é do processo ser estacionário ao entorno de uma tendência determinística, simplificamos com <span class="math inline">H_0: y_t \tilde{} I(0)</span> enquanto que a do PP é de raíz unitária. Então, para confirmarmos nossa intuição, o p-valor de um deve ser baixo e do outro deve ser alto.</p>
<div class="cell">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>dplyr<span class="sc">::</span><span class="fu">bind_rows</span>(</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a><span class="fu">list</span>(</span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( ptr_br_log, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)),</span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( ipca_log, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)),</span>
<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( petro_log, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)),</span>
<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( cambio_log, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)) )) <span class="sc">|></span></span>
<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">bind_cols</span>(<span class="st">"Variável"</span> <span class="ot">=</span><span class="fu">c</span>(<span class="st">"Log Petro Br"</span>, <span class="st">"Log IPCA"</span>, <span class="st">"Log Petro"</span>, <span class="st">"Log Câmbio"</span>)) <span class="sc">|></span> </span>
<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">select</span>(Variável, <span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>) <span class="sc">|></span> <span class="fu">set_tab</span>(<span class="at">cap_tab =</span> <span class="st">"Resultado do KPSS e PP"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<table class="table table-striped table-hover table-condensed table-responsive" style="width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Resultado do KPSS e PP</caption>
<thead>
<tr>
<th style="text-align:left;"> Variável </th>
<th style="text-align:right;"> kpss_stat </th>
<th style="text-align:right;"> kpss_pvalue </th>
<th style="text-align:right;"> pp_stat </th>
<th style="text-align:right;"> pp_pvalue </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;"> Log Petro Br </td>
<td style="text-align:right;"> 4.7685 </td>
<td style="text-align:right;"> 0.01 </td>
<td style="text-align:right;"> -1.0282 </td>
<td style="text-align:right;"> 0.1000 </td>
</tr>
<tr>
<td style="text-align:left;"> Log IPCA </td>
<td style="text-align:right;"> 5.6641 </td>
<td style="text-align:right;"> 0.01 </td>
<td style="text-align:right;"> -3.2122 </td>
<td style="text-align:right;"> 0.0265 </td>
</tr>
<tr>
<td style="text-align:left;"> Log Petro </td>
<td style="text-align:right;"> 3.6723 </td>
<td style="text-align:right;"> 0.01 </td>
<td style="text-align:right;"> -1.5830 </td>
<td style="text-align:right;"> 0.1000 </td>
</tr>
<tr>
<td style="text-align:left;"> Log Câmbio </td>
<td style="text-align:right;"> 3.5262 </td>
<td style="text-align:right;"> 0.01 </td>
<td style="text-align:right;"> -1.0455 </td>
<td style="text-align:right;"> 0.1000 </td>
</tr>
</tbody>
</table>
</div>
</div>
<p>Portanto, rejeitamos a hipótese nula do KPSS de estacionariedade ao entorno de uma tendência determinística a favor da hipótese alternativa de raíz unitária para todas as variáveis, a 5% de significância. Aceitamos a nula do teste PP de integração de primeira ordem, ou seja, uma raíz unitária, a 5%, para todas as variáveis <strong>exceto</strong> para o IPCA. As confirmações de nossa inspeção visual indicam que deveremos ter um VAR com variáveis diferenciadas. A seguir, vamos criar novas variáveis diferenciadas e repetir o teste, além de retirar o tempo de regime de câmbio fixo:</p>
<div class="cell">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>dd <span class="ot"><-</span> dd <span class="sc">|></span> </span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">mutate</span>(</span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a> <span class="at">ptr_br_log_dif =</span> <span class="fu">difference</span>(ptr_br_log, <span class="at">lag =</span> <span class="dv">1</span>),</span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a> <span class="at">ipca_log_dif =</span> <span class="fu">difference</span>(ipca_log, <span class="at">lag =</span> <span class="dv">1</span>),</span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a> <span class="at">petro_log_dif =</span> <span class="fu">difference</span>(petro_log, <span class="at">lag =</span> <span class="dv">1</span>),</span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a> <span class="at">cambio_log_dif =</span> <span class="fu">difference</span>(cambio_log, <span class="at">lag =</span> <span class="dv">1</span>),</span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a> <span class="at">ptr_br_log_dif12 =</span> <span class="fu">difference</span>(ptr_br_log, <span class="at">lag =</span> <span class="dv">12</span>),</span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a> <span class="at">ipca_log_dif12 =</span> <span class="fu">difference</span>(ipca_log, <span class="at">lag =</span> <span class="dv">12</span>),</span>
<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a> <span class="at">petro_log_dif12 =</span> <span class="fu">difference</span>(petro_log, <span class="at">lag =</span> <span class="dv">12</span>),</span>
<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a> <span class="at">cambio_log_dif12 =</span> <span class="fu">difference</span>(cambio_log, <span class="at">lag =</span> <span class="dv">12</span>)) <span class="sc">|></span></span>
<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">filter</span>(<span class="sc">!</span><span class="fu">is.na</span>(petro_log_dif12))</span>
<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a>dd <span class="ot"><-</span> dd <span class="sc">|></span> <span class="fu">filter</span>(dt <span class="sc">>=</span> lubridate<span class="sc">::</span><span class="fu">my</span>(<span class="st">"Jul 1999"</span>))</span>
<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a><span class="fu">attach</span>(dd)</span>
<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a>dplyr<span class="sc">::</span><span class="fu">bind_rows</span>(</span>
<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a><span class="fu">list</span>(</span>
<span id="cb15-18"><a href="#cb15-18" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( ptr_br_log_dif, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)),</span>
<span id="cb15-19"><a href="#cb15-19" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( ipca_log_dif, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)),</span>
<span id="cb15-20"><a href="#cb15-20" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( petro_log_dif, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)),</span>
<span id="cb15-21"><a href="#cb15-21" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> <span class="fu">features</span>( cambio_log_dif, <span class="fu">c</span>(unitroot_kpss, unitroot_pp)) )) <span class="sc">|></span></span>
<span id="cb15-22"><a href="#cb15-22" aria-hidden="true" tabindex="-1"></a> <span class="fu">bind_cols</span>(<span class="st">"Variável"</span> <span class="ot">=</span><span class="fu">c</span>(<span class="st">"Log Dif(-1) Petro Br"</span>, <span class="st">"Log Dif(-1) IPCA"</span>, <span class="st">"Log Dif(-1) Petro"</span>, <span class="st">"Log Dif(-1) Câmbio"</span>)) <span class="sc">|></span> </span>
<span id="cb15-23"><a href="#cb15-23" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">select</span>(Variável, <span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>) <span class="sc">|></span> <span class="fu">set_tab</span>(<span class="at">cap_tab =</span> <span class="st">"Resultado do KPSS e PP"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<table class="table table-striped table-hover table-condensed table-responsive" style="width: auto !important; margin-left: auto; margin-right: auto;">
<caption>Resultado do KPSS e PP</caption>
<thead>
<tr>
<th style="text-align:left;"> Variável </th>
<th style="text-align:right;"> kpss_stat </th>
<th style="text-align:right;"> kpss_pvalue </th>
<th style="text-align:right;"> pp_stat </th>
<th style="text-align:right;"> pp_pvalue </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;"> Log Dif(-1) Petro Br </td>
<td style="text-align:right;"> 0.0802 </td>
<td style="text-align:right;"> 0.1 </td>
<td style="text-align:right;"> -13.4414 </td>
<td style="text-align:right;"> 0.01 </td>
</tr>
<tr>
<td style="text-align:left;"> Log Dif(-1) IPCA </td>
<td style="text-align:right;"> 0.2270 </td>
<td style="text-align:right;"> 0.1 </td>
<td style="text-align:right;"> -7.8199 </td>
<td style="text-align:right;"> 0.01 </td>
</tr>
<tr>
<td style="text-align:left;"> Log Dif(-1) Petro </td>
<td style="text-align:right;"> 0.0857 </td>
<td style="text-align:right;"> 0.1 </td>
<td style="text-align:right;"> -11.7787 </td>
<td style="text-align:right;"> 0.01 </td>
</tr>
<tr>
<td style="text-align:left;"> Log Dif(-1) Câmbio </td>
<td style="text-align:right;"> 0.1454 </td>
<td style="text-align:right;"> 0.1 </td>
<td style="text-align:right;"> -11.2043 </td>
<td style="text-align:right;"> 0.01 </td>
</tr>
</tbody>
</table>
</div>
</div>
<p>Agora temos certeza que uma diferenciação basta para a estacionariedade das variáveis: aceitamos a hipótese nula do KPSS e a alternativa do PP para todas a variáveis. Nosso VAR terá a primeira diferença, somente. A seguir, as variáveis transformadas:</p>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>plt_cambio <span class="ot"><-</span> <span class="fu">plot_ly</span>(dd,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span><span class="fu">as.Date</span>(dt), <span class="at">y =</span> <span class="sc">~</span>cambio_log_dif,</span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Câmbio"</span>,</span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#30d5c8"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'Primeira Diferença do Log da Taxa de Câmbio Comercial R$ '</span>,</span>
<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb16-8"><a href="#cb16-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb16-9"><a href="#cb16-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb16-10"><a href="#cb16-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb16-11"><a href="#cb16-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb16-12"><a href="#cb16-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">"Dif Log R$/US$"</span>,</span>
<span id="cb16-13"><a href="#cb16-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb16-14"><a href="#cb16-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb16-15"><a href="#cb16-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb16-16"><a href="#cb16-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb16-17"><a href="#cb16-17" aria-hidden="true" tabindex="-1"></a>plt_cambio</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div class="plotly html-widget html-fill-item-overflow-hidden html-fill-item" id="htmlwidget-b78f72c88f07ca33e187" style="width:100%;height:505px;"></div>
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</div>
</div>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>plt_ipca <span class="ot"><-</span> <span class="fu">plot_ly</span>(dd,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span><span class="fu">as.Date</span>(dt), <span class="at">y =</span> <span class="sc">~</span>ipca_log_dif,</span>
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"IPCA"</span>,</span>
<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#551a8b"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'Primeira Diferença do Log da IPCA, Brasil, de Jul/95 a Jul/2022.'</span>,</span>
<span id="cb17-7"><a href="#cb17-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb17-8"><a href="#cb17-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb17-9"><a href="#cb17-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb17-10"><a href="#cb17-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb17-11"><a href="#cb17-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb17-12"><a href="#cb17-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">"Dif Log IPCA"</span>,</span>
<span id="cb17-13"><a href="#cb17-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb17-14"><a href="#cb17-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb17-15"><a href="#cb17-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb17-16"><a href="#cb17-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb17-17"><a href="#cb17-17" aria-hidden="true" tabindex="-1"></a>plt_ipca</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div class="plotly html-widget html-fill-item-overflow-hidden html-fill-item" id="htmlwidget-71e178674219efb63cbb" style="width:100%;height:505px;"></div>
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</div>
</div>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>plt_petro <span class="ot"><-</span> <span class="fu">plot_ly</span>(dd,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span><span class="fu">as.Date</span>(dt), <span class="at">y =</span> <span class="sc">~</span>petro_log_dif,</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Petroleum"</span>,</span>
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#2E8B57"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'Primeira Diferença do Log da Média do Preço Internacional do Petróleo'</span>,</span>
<span id="cb18-7"><a href="#cb18-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb18-8"><a href="#cb18-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb18-9"><a href="#cb18-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb18-10"><a href="#cb18-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb18-11"><a href="#cb18-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb18-12"><a href="#cb18-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">"Dif Log Preço em Dólar"</span>,</span>
<span id="cb18-13"><a href="#cb18-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb18-14"><a href="#cb18-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb18-15"><a href="#cb18-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb18-16"><a href="#cb18-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb18-17"><a href="#cb18-17" aria-hidden="true" tabindex="-1"></a>plt_petro</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
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<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>plt_petro_n <span class="ot"><-</span> <span class="fu">plot_ly</span>(dd,<span class="at">type =</span> <span class="st">'scatter'</span>, <span class="at">mode =</span> <span class="st">'lines'</span>) <span class="sc">|></span> </span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">add_trace</span>(<span class="at">x =</span> <span class="sc">~</span><span class="fu">as.Date</span>(dt), <span class="at">y =</span> <span class="sc">~</span>ptr_br_log_dif,</span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">" Dif Petroleum (R$)"</span>,</span>
<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a> <span class="at">line =</span> <span class="fu">list</span>(<span class="at">color =</span> <span class="st">"#073320"</span>, <span class="at">width =</span> <span class="dv">2</span>)) <span class="sc">|></span> </span>
<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">layout</span>(<span class="at">showlegend =</span> F,</span>
<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a> <span class="at">title=</span><span class="st">'Primeira Diferença do Log da Média do Preço Internacional do Petróleo, em Reais'</span>,</span>
<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a> <span class="at">xaxis =</span> <span class="fu">list</span>(<span class="at">rangeslider =</span> <span class="fu">list</span>(<span class="at">visible =</span> T),</span>
<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="st">"Data"</span>,</span>
<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb19-10"><a href="#cb19-10" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb19-11"><a href="#cb19-11" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb19-12"><a href="#cb19-12" aria-hidden="true" tabindex="-1"></a> <span class="at">yaxis =</span> <span class="fu">list</span>(<span class="at">title =</span> <span class="st">" Dif Log Preço em Reais"</span>,</span>
<span id="cb19-13"><a href="#cb19-13" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinecolor =</span> <span class="st">'#ffff'</span>,</span>
<span id="cb19-14"><a href="#cb19-14" aria-hidden="true" tabindex="-1"></a> <span class="at">zerolinewidth =</span> <span class="dv">2</span>,</span>
<span id="cb19-15"><a href="#cb19-15" aria-hidden="true" tabindex="-1"></a> <span class="at">gridcolor =</span> <span class="st">'ffff'</span>),</span>
<span id="cb19-16"><a href="#cb19-16" aria-hidden="true" tabindex="-1"></a> <span class="at">plot_bgcolor=</span><span class="st">'#e5ecf6'</span>)</span>
<span id="cb19-17"><a href="#cb19-17" aria-hidden="true" tabindex="-1"></a>plt_petro_n</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
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</div>
</div>
</section>
<section id="funções-de-autocorrelações" class="level1" data-number="5">
<h1 data-number="5"><span class="header-section-number">5</span> Funções de Autocorrelações</h1>
<p>Faremos as funções de autocorrelação (FAC e FACP) para cada variável para perceber quais lags da própria variável ou de seus erros são relevantes para explicar sua trajetória. É possível que o n-ésimo lag de uma variável seja relevante para explicá-la mas, passando para o VAR, esse n-ésimo lag não seja considerado. Essa desconsideração pode aparecer no erro do VAR, a depender da relevância do lag. Conhecer as propiedades de cada variável,individualmente, ajuda a entender o modelo multivariado. A análise das funções também pode nos indicar usar a diferenciação com o evento imediatamente anterior em detrimento da diferenciação com o mesmo mês do ano anterior, fica como exercício avaliar os gráficos das variáveis <code><>_dif12</code>, criadas anteriormente.</p>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggarrange</span>(</span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">ACF</span>(ptr_br_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> ggplot2<span class="sc">::</span><span class="fu">autoplot</span>(),</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">PACF</span>(ptr_br_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> ggplot2<span class="sc">::</span><span class="fu">autoplot</span>()</span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a>,<span class="at">labels =</span> <span class="st">"F.A.'s de Dif(Log(Petro R$))"</span></span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-16-1.png" class="img-fluid figure-img" width="864"></p>
</figure>
</div>
</div>
</div>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggarrange</span>(</span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">ACF</span>(ipca_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> <span class="fu">autoplot</span>(),</span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">PACF</span>(ipca_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> <span class="fu">autoplot</span>()</span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a>,<span class="at">labels =</span> <span class="st">"F.A.'s de Dif(Log(IPCA))"</span></span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a>) <span class="co"># Maior influnência do passado na contemporânea</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-17-1.png" class="img-fluid figure-img" width="864"></p>
</figure>
</div>
</div>
</div>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb22"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggarrange</span>(</span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">ACF</span>(petro_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> <span class="fu">autoplot</span>(),</span>
<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">PACF</span>(petro_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> <span class="fu">autoplot</span>()</span>
<span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a>,<span class="at">labels =</span> <span class="st">"F.A.'s de Dif(Log(Petro US$))"</span></span>
<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-18-1.png" class="img-fluid figure-img" width="864"></p>
</figure>
</div>
</div>
</div>
<div class="cell" data-layout-align="center">
<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggarrange</span>(</span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">ACF</span>(cambio_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> <span class="fu">autoplot</span>(),</span>
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a>dd <span class="sc">|></span> feasts<span class="sc">::</span><span class="fu">PACF</span>(cambio_log_dif, <span class="at">lag_max =</span> <span class="dv">36</span>) <span class="sc">|></span> <span class="fu">autoplot</span>()</span>
<span id="cb23-4"><a href="#cb23-4" aria-hidden="true" tabindex="-1"></a>,<span class="at">labels =</span> <span class="st">"F.A.'s de Dif(Log(R$/US$))"</span></span>
<span id="cb23-5"><a href="#cb23-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="report_files/figure-html/unnamed-chunk-19-1.png" class="img-fluid figure-img" width="864"></p>
</figure>
</div>
</div>
</div>
<p>As FAC’s nos mostram erros com comportamento senoide em todas as variáveis, com alta persistência para os erros do IPCA, e algumas significâncias assíncronas (sem múltiplos) no componente autorregressivo, o que dificulta a visualização de sazonalidades.</p>
</section>
<section id="var" class="level1" data-number="6">
<h1 data-number="6"><span class="header-section-number">6</span> VAR</h1>
<p>Primeiramente, definimos a ordem do conjunto VAR. Para fins de comparação, vamos montar dois modelos: o <strong>primeiro modelo</strong> com Petro US$, Câmbio e IPCA; <strong>o segundo</strong> com Petro R$ e IPCA. Separar o efeito do câmbio e do preço do petróleo pode ser valioso na fase de decomposição da variância e por capturar o efeito puro do preço internacional do petróleo: quando fazemos <code>petro * câmbio</code>, todos os demais fatores que afetam o câmbio (como saúde fiscal ou taxa de juros do FED) também afetarão o preço percebido do petróleo no país.</p>
<p>A regra para determinar a ordem do sistema é colocar tantas defasagens forem necessárias para produzir resíduos brancos em todas as variáveis, mas adicionar muitos parâmetros diminui o poder dos testes estatísticos. Devemos usar algum critério de informação para escolher a ordem do sistema, penalizando lags que não contribuem significativamente para a explicação dos erros. Os critérios HQ() e SC() penalizam mais fortemente parâmetros adicionais, enquanto que o AIC() tende a sobreparametrizar o modelo, apesar de funcionar melhor em pequenas amostras, o que não é o caso.</p>
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<summary>Code</summary>
<div class="sourceCode cell-code" id="cb24"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a>var1_p_select <span class="ot"><-</span> <span class="fu">VARselect</span>(</span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> dplyr<span class="sc">::</span><span class="fu">as_tibble</span>() <span class="sc">|></span></span>
<span id="cb24-3"><a href="#cb24-3" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">select</span>(ipca_log_dif, petro_log_dif, cambio_log_dif),</span>
<span id="cb24-4"><a href="#cb24-4" aria-hidden="true" tabindex="-1"></a> <span class="at">lag.max =</span> <span class="dv">12</span>,</span>
<span id="cb24-5"><a href="#cb24-5" aria-hidden="true" tabindex="-1"></a> <span class="at">season =</span> <span class="dv">12</span>,</span>
<span id="cb24-6"><a href="#cb24-6" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"both"</span>)</span>
<span id="cb24-7"><a href="#cb24-7" aria-hidden="true" tabindex="-1"></a>var1_p_select<span class="sc">$</span>selection <span class="sc">|></span> <span class="fu">t</span>() <span class="sc">|></span> <span class="fu">set_tab</span>(<span class="at">cap_tab =</span> <span class="st">"VAR 1: Petro US$, Câmbio e IPCA"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
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<table class="table table-striped table-hover table-condensed table-responsive" style="width: auto !important; margin-left: auto; margin-right: auto;">
<caption>VAR 1: Petro US$, Câmbio e IPCA</caption>
<thead>
<tr>
<th style="text-align:right;"> AIC(n) </th>
<th style="text-align:right;"> HQ(n) </th>
<th style="text-align:right;"> SC(n) </th>
<th style="text-align:right;"> FPE(n) </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 4 </td>
<td style="text-align:right;"> 1 </td>
<td style="text-align:right;"> 1 </td>
<td style="text-align:right;"> 4 </td>
</tr>
</tbody>
</table>
</div>
</div>
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<details open="">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>var2_p_select <span class="ot"><-</span> <span class="fu">VARselect</span>(</span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> dplyr<span class="sc">::</span><span class="fu">as_tibble</span>() <span class="sc">|></span></span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">select</span>(ipca_log_dif, ptr_br_log_dif),</span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a> <span class="at">lag.max =</span> <span class="dv">12</span>,</span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a> <span class="at">season =</span> <span class="dv">12</span>,</span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"both"</span>)</span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a>var2_p_select<span class="sc">$</span>selection <span class="sc">|></span> <span class="fu">t</span>() <span class="sc">|></span> <span class="fu">set_tab</span>(<span class="at">cap_tab =</span> <span class="st">"VAR 2: Petro R$ e IPCA"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<table class="table table-striped table-hover table-condensed table-responsive" style="width: auto !important; margin-left: auto; margin-right: auto;">
<caption>VAR 2: Petro R$ e IPCA</caption>
<thead>
<tr>
<th style="text-align:right;"> AIC(n) </th>
<th style="text-align:right;"> HQ(n) </th>
<th style="text-align:right;"> SC(n) </th>
<th style="text-align:right;"> FPE(n) </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 4 </td>
<td style="text-align:right;"> 1 </td>
<td style="text-align:right;"> 1 </td>
<td style="text-align:right;"> 4 </td>
</tr>
</tbody>
</table>
</div>
</div>
<p>Vamos rodar os dois modelos com VAR(1) e sem dummies sazonais. Fica como exercício comparar o ganho de explicação e as significâncias com p=4.</p>
<section id="var_1-petro-us-câmbio-e-ipca" class="level2" data-number="6.1">
<h2 data-number="6.1" class="anchored" data-anchor-id="var_1-petro-us-câmbio-e-ipca"><span class="header-section-number">6.1</span> <span class="math inline">VAR_{1}</span>: Petro US$, Câmbio e IPCA</h2>
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<summary>Code</summary>
<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a>var1 <span class="ot"><-</span> vars<span class="sc">::</span><span class="fu">VAR</span>(</span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a> dd <span class="sc">|></span> dplyr<span class="sc">::</span><span class="fu">as_tibble</span>() <span class="sc">|></span></span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a> dplyr<span class="sc">::</span><span class="fu">select</span>(ipca_log_dif, cambio_log_dif, petro_log_dif),</span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a> <span class="at">p =</span> <span class="dv">1</span>,</span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a> <span class="at">type =</span> <span class="st">"const"</span>,</span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a> <span class="at">season =</span> <span class="cn">NULL</span>,</span>
<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a> <span class="at">exog =</span> <span class="cn">NULL</span>)</span>
<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(var1)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code>
VAR Estimation Results:
=========================
Endogenous variables: ipca_log_dif, cambio_log_dif, petro_log_dif
Deterministic variables: const
Sample size: 275
Log Likelihood: 2011.68
Roots of the characteristic polynomial:
0.6242 0.4388 0.1376
Call:
vars::VAR(y = dplyr::select(dplyr::as_tibble(dd), ipca_log_dif,
cambio_log_dif, petro_log_dif), p = 1, type = "const", exogen = NULL)
Estimation results for equation ipca_log_dif:
=============================================
ipca_log_dif = ipca_log_dif.l1 + cambio_log_dif.l1 + petro_log_dif.l1 + const
Estimate Std. Error t value Pr(>|t|)
ipca_log_dif.l1 0.6336983 0.0477546 13.270 < 2e-16 ***
cambio_log_dif.l1 0.0182740 0.0050916 3.589 0.000394 ***
petro_log_dif.l1 0.0060105 0.0020802 2.889 0.004172 **
const 0.0017625 0.0003138 5.616 4.84e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.003083 on 271 degrees of freedom
Multiple R-Squared: 0.4081, Adjusted R-squared: 0.4016
F-statistic: 62.28 on 3 and 271 DF, p-value: < 2.2e-16
Estimation results for equation cambio_log_dif:
===============================================
cambio_log_dif = ipca_log_dif.l1 + cambio_log_dif.l1 + petro_log_dif.l1 + const
Estimate Std. Error t value Pr(>|t|)
ipca_log_dif.l1 -0.425754 0.562229 -0.757 0.4496
cambio_log_dif.l1 0.318697 0.059945 5.317 2.21e-07 ***
petro_log_dif.l1 -0.050679 0.024491 -2.069 0.0395 *