<div dir="auto"><div>Granger e Newbold abordaram este fenômeno em 1974. A econometria de séries temporais foi desenvolvida nas pesquisas subsequentes, desenbocando no desevolvimento da análise de cointegração e culminando com o Nobel de economia para Engle e Granger no início dos anos 2000.<div dir="auto"><br></div><div dir="auto">Abraços, Marcelo Rubens</div><div dir="auto"><br></div><br><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Em sex, 5 de mar de 2021 10:12, Basilio de Bragança Pereira <<a href="mailto:basilio@hucff.ufrj.br">basilio@hucff.ufrj.br</a>> escreveu:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto">Sobre assunto correlato sugiro olhar na Wikipédia os dados e gráficos de <div>Anscombe ‘s quartet<br><br><div id="m_5990300652247223803AppleMailSignature" dir="ltr">Enviado do meu iPhone</div><div dir="ltr"><br>Em 5 de mar de 2021, à(s) 10:01, Julio Stern <<a href="mailto:jmstern@hotmail.com" target="_blank" rel="noreferrer">jmstern@hotmail.com</a>> escreveu:<br><br></div><blockquote type="cite"><div dir="ltr">
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<span style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt;font-family:Arial,Helvetica,sans-serif">Caros Redistas </span></span></div>
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<span style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt;font-family:Arial,Helvetica,sans-serif">Conversando com colegas de outras areas sobre a diferenca entre Causalidade e Correlacao, </span></span><span style="color:rgb(0,0,0);font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">principalmente
no contexto de vacinas, tratamentos medicos para Covid, etc. </span></span><span style="color:rgb(0,0,0);font-family:Calibri,Helvetica,sans-serif;font-size:12pt"><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">acabei conhecendo o</span></span><span lang="PT-BR" style="color:rgb(0,0,0);font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> livro: </span></div>
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<span lang="PT-BR" style="color:rgb(0,0,0);font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span><span lang="PT-BR" style="color:rgb(0,0,0);font-family:Calibri,sans-serif;font-size:11pt"><span style="font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></div>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">>>></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Tyler
Vigen (2015).</span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Spurious Correlations.</span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Hachette
Books.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">que tem gráficos fantasticos, com series temporais totalmente desconexas que exibem altíssima correlacao.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Nao tenho o livro, mas alguns graficos podem ser vistos em<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">>>> <a href="https://www.tylervigen.com/spurious-correlations" target="_blank" rel="noreferrer">https://www.tylervigen.com/spurious-correlations</a></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">>>> <a href="https://tylervigen.com/discover" target="_blank" rel="noreferrer">https://tylervigen.com/discover</a></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Comecei a fazer umas continhas rapidas sobre a probabilidade, p</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> , </span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">de
obter, em duas series temporais, x(t) e y(t) ,<span> </span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">com dez pontos de abscissa t={1,2, ... 10}</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">e
ordenada no intervalo [0,1] , uma alta correlação, i.e.,<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">p = Pr ( corr ( x(t) , y(t) )<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">>=</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">(1-alpha)
) , para alpha= 0.1</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">ou</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">0.05<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">ou</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">0.01</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Assumindo nao haver estrutura alguma nas series x(t) e y(t) , o resultado eh muito baixo.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Mesmo considerando uma enorme biblioteca de graficos aleatorios, nao da...<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Parece ser necessario assumir "a priori" a existência de alguma "estrutura intrinseca de associacao" entre os pontos de cada uma das series temporais,
por exemplo, alguma estrutura de auto-correlacao.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Antes de sair por ai tentando reinventar a roda, melhor perguntar a quem sabe...<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Alguem ja deve ter pensado neste problema!<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span><span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Alguma
ideia de como modela-lo?<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">Abraco a todos e tudo de bom,<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif">---Julio Stern<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px;font-size:14pt;line-height:normal;font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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