<div dir="ltr"><div class="gmail_default" style="font-family:monospace,monospace">Caros,</div><div class="gmail_default" style="font-family:monospace,monospace"><br></div><div class="gmail_default" style="font-family:monospace,monospace">Apenas adicionando um texto a mais na discussão "Causalidade x Correlação". Segue o link de um texto do Judea Pearl sobre o paradoxo de Simpson, no qual ele discute relações espúrias como função de uma terceira variável.</div><div class="gmail_default" style="font-family:monospace,monospace"><br></div><div class="gmail_default" style="font-family:monospace,monospace"><a href="https://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf">https://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf</a><br></div><div class="gmail_default" style="font-family:monospace,monospace"><br></div><div class="gmail_default" style="font-family:monospace,monospace">Abs</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Em sáb., 6 de mar. de 2021 às 06:56, Julio Stern <<a href="mailto:jmstern@hotmail.com">jmstern@hotmail.com</a>> escreveu:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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<span style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt">Sobre e-valores / FBST para problemas de Cointegracao: </span></span>
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<div style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt">O artigo do Marcio Alves Diniz (2020), citado na ultima mensagem, tem a desvantagem de ser um tanto sofisticado. </span></div>
<div style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt">Todavia, serve para explicar algumas coisas muito importantes. </span></div>
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<div style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt">Testes de Raiz Unitaria e testes de Cointegracao sempre foram problematicos para Estatistica Bayesiana. </span></div>
<div style="margin:0px;font-size:12pt;background-color:rgb(255,255,255)"><span style="margin:0px;font-size:14pt">Alguem que queira utilizar testes baseados em Fatores de Bayes (Bayes Factors) tem que tomar muito cuidado, </span><span style="margin:0px;font-size:14pt">para
nao virar um Credulo (aquele que enxerga cointegracao em toda parte) ou um Cetico (aquele que nunca admite cointegracao). </span><span style="margin:0px;font-size:14pt"> </span></div>
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<span style="margin:0px;font-size:14pt">Eh preciso "cozinhar" prioris especiais (chimeras ou ad-hoceries como dizia o I.J. Good) para "arrumar" as conclusoes a que se chega -- um horror. </span></div>
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<span style="margin:0px;font-size:14pt">Com o e-valor / FBST tudo se resolve naturalmente. </span></div>
<div style="margin:0px;font-size:12pt;font-family:Calibri,Helvetica,sans-serif;color:rgb(0,0,0)">
<span style="margin:0px;font-size:14pt">Quem quiser utilizar a priory de Jeffreys, que eh uma entidade Covariante (ou "invariante" em uma linguagem mais relaxada) por transformacoes de coordenadas, pode faze-lo sem problemas. </span></div>
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<span style="margin:0px;font-size:14pt">O trabalho de doutorado do Marcio foi exatamente o de desenvolver esta theoria. </span><br>
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<span style="margin:0px;font-size:14pt">Tivemos grande dificuldade para publicar os primeiros artigos em boas revistas, justamente por abstermo-nos de usar chimeras como prioris ad-hoc necessarias para "ajeitar" o processo de inferencia via Fatores de Bayes. </span></div>
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<span style="margin:0px;font-size:14pt">Um grande nome na area me disse - na cara dura: Se depender de mim, voces nunca publicarao este artigo, pois suas conclusoes invalidam muitos artigos previamente publicados, varios deles por mim mesmo! Agradeci a honestidade
da resposta... </span></div>
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<span style="margin:0px;font-size:14pt">Testes de Raiz Unitaria e Cointegracao sao uma area fascinante de pesquisa em Estatistica, uma area que tem, como poucas,<span> </span><span style="margin:0px;background-color:rgb(255,255,255);display:inline">o
poder </span>de revelar paradoxos. </span></div>
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<span style="margin:0px;font-size:14pt">Abracos virtuais e Tudo de bom, </span></div>
<span style="margin:0px;font-size:12pt;font-family:Calibri,Helvetica,sans-serif;color:rgb(0,0,0)"><span style="margin:0px;font-size:14pt">---Julio Stern </span></span></div>
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<div id="gmail-m_8830086143828264191divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Hedibert Lopes <<a href="mailto:hedibert@gmail.com" target="_blank">hedibert@gmail.com</a>><br>
<b>Sent:</b> Friday, March 5, 2021 8:34 PM<br>
<b>To:</b> Diego Samuel Rodrigues <<a href="mailto:diegosarodrigues@gmail.com" target="_blank">diegosarodrigues@gmail.com</a>><br>
<b>Cc:</b> Julio Stern <<a href="mailto:jmstern@hotmail.com" target="_blank">jmstern@hotmail.com</a>>; <a href="mailto:abe@lists.ime.usp.br" target="_blank">abe@lists.ime.usp.br</a> <<a href="mailto:abe@lists.ime.usp.br" target="_blank">abe@lists.ime.usp.br</a>><br>
<b>Subject:</b> Re: [ABE-L] Fw: Causalidade X Correlacao</font>
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<div dir="ltr">Boa tarde pessoal,
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<div>Aproveitando o gancho do Diego pra dizer que para mim a discussão acerca de correlação/causação parece a discussão acerca de valores. Correlação é uma de um universo grande de medidas de associação entre variáveis aleatórias, só que bem famosa! P-value
é uma forma, também famosa, de "tentar" discriminar com relação a uma determinada hipótese científica. Ambos têm mais defeitos que qualidades, mas seguem sendo bastante usados.
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<div>Aproveito pra divulgar umas compilações que venho fazendo....<a href="http://hedibert.org/compilations/.....com" target="_blank">http://hedibert.org/compilations/.....com</a> particular ênfase em duas delas:</div>
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<ol style="margin:0px 0px 21px 20px;padding:0px;border:0px;font-variant-numeric:inherit;font-variant-east-asian:inherit;font-stretch:inherit;font-size:14px;line-height:inherit;font-family:Helvetica,Arial,sans-serif;vertical-align:baseline;list-style-position:initial;color:rgb(101,112,123)">
<li style="margin:0px 0px 14px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;font-size:inherit;line-height:18px;font-family:inherit;vertical-align:baseline">
<a href="http://hedibert.org/wp-content/uploads/2015/10/causality-meeting1.pdf" style="margin:0px;padding:0px;border:0px;font:inherit;vertical-align:baseline;color:rgb(0,147,208);text-decoration-line:none;outline:0px" target="_blank">Causality: Readings in Statistics
and Econometrics (2015)</a> + annotated bibliography <a href="http://hedibert.org/wp-content/uploads/2015/10/annotatedbibliography.pdf" style="margin:0px;padding:0px;border:0px;font:inherit;vertical-align:baseline;color:rgb(0,147,208);text-decoration-line:none;outline:0px" target="_blank">here</a> & <a href="http://hedibert.org/wp-content/uploads/2015/10/annotatedbibliography-articles.pdf" style="margin:0px;padding:0px;border:0px;font:inherit;vertical-align:baseline;color:rgb(0,147,208);text-decoration-line:none;outline:0px" target="_blank">here</a></li><li style="margin:0px 0px 14px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;font-size:inherit;line-height:18px;font-family:inherit;vertical-align:baseline">
<a href="http://hedibert.org/wp-content/uploads/2021/02/discussion-about-pvalue-referencelist-by-hedibertlopes.pdf" style="margin:0px;padding:0px;border:0px;font:inherit;vertical-align:baseline;color:rgb(129,215,66);text-decoration-line:none;outline:0px" target="_blank">Discussion
about p-values (2021)</a></li></ol>
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<div>Abs e bom final de semana a todos,</div>
<div>Hedibert</div>
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<div dir="ltr">On Fri, Mar 5, 2021 at 5:22 PM Diego Samuel Rodrigues <<a href="mailto:diegosarodrigues@gmail.com" target="_blank">diegosarodrigues@gmail.com</a>> wrote:<br>
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<div dir="ltr">Olá a todos, boa tarde.<br>
<br>
A despeito de parecer que a discussão se encerrou, se permitem um comentário de um não-estatístico, o assunto "Correlação x Causalidade" me fez lembrar de um artigo relevante sobre assunto, do qual destaco o trecho que coloco mais abaixo.
<div><br>
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<div>Saudações,<br>
<br>
Diego Samuel Rodrigues</div>
<div>Faculdade de Tecnologia, Universidade Estadual de Campinas</div>
<div><br>
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<div>=====</div>
<div><br>
<b>Detecting Causality in Complex Ecosystems</b><br>
</div>
<div>George Sugihara et al.</div>
<div><i>Science </i><b>338</b>, 496 (2012)</div>
<div><a href="http://doi.org/10.1126/science.1227079" target="_blank">doi.org/10.1126/science.1227079</a><br>
<br>
<i>Although correlation is neither necessary nor sufficient to establish causation, it remains deeply ingrained in our heuristic thinking (8, 13, 16, 17). One might conclude, for example, that the variables in Fig. 1 have no causal relation because they are
uncorrelated. Obviously, lack of correlation does not imply lack of causation. Because of this and for reasons just given, the use of correlation to infer causation is risky, especially as we come to recognize that nonlinear dynamics are ubiquitous.</i><br>
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<div dir="ltr">Em sex., 5 de mar. de 2021 às 14:49, Julio Stern <<a href="mailto:jmstern@hotmail.com" target="_blank">jmstern@hotmail.com</a>> escreveu:<br>
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<span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">Caro Pedro: </span></div>
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<span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">Grato pela refereincia: </span></div>
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<span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">>>> Pedro Morettin (2017). </span><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">Econometria Financeira, Capítulo 10. </span></div>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">Esta eh uma boa referencia, sempre correta, mas ao mesmo tempo didatica e facil de entender. </span></div>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">Caro Hedibert: </span></div>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">Grato pela referencia: </span></div>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><br>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">>>> </span><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">Michael
Murray, “A Drunk and Her Dog: An Illustration of Cointegration and Error Correction,” American Statistician, 48, no. 1 (1994): 37–39. </span><span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><br>
<span style="margin:0px"></span></span><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline"> </span></div>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">Este eh um paper escrito exatamente no espirito que eu queria, infelizmente, nao exatamente sobre o problema que eu queria... Mas eh este
tipo de coisa que eu preciso para dialogar meu publico alvo. </span></div>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">Canhao para matar mosca: </span></div>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">A turma do FBST / e-valor tem seus canhoes para teste de cointegracao, vide: </span></div>
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<span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;background-color:rgb(255,255,255);display:inline">>>> </span><span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">Marcio
Alves Diniz, Carlos Alberto de Braganca Pereira, Julio Michael Stern (2020). </span><a href="https://www.ime.usp.br/~jmstern/wp-content/uploads/2020/10/Din20.Ent.pdf" style="box-sizing:border-box;background:transparent;color:rgb(61,126,122);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px" target="_blank"><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif"> </span><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">Cointegration
and Unit Root Tests: A Fully Bayesian Approach. Entropy, 22, 9, 968. </span></a><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;display:inline"><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif"> </span></span><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">doi:</span><a href="https://www.mdpi.com/1099-4300/22/9/968" style="box-sizing:border-box;background:transparent;color:rgb(61,126,122);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px" target="_blank"><span style="font-size:14pt;font-family:Arial,Helvetica,sans-serif">10.3390/e22090968</span></a><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;display:inline"><br>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">Da para usar este canhao para "explicar" um monte de coisas interessantes na area, so que a
explicacaco eh totalmente intragavel para quem ja nao entende de antemao muita coisa de estatistica... Neste sentido, nao resolve o problema que tenho que resolver :-) </span><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline"> </span></span></div>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;display:inline"><br>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">Faltam mais artigos sobre o assunto escritos como o artigo do Murray... </span></span></div>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;display:inline"><br>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">Grato a todos que me responderam, inclusive com copia do Livro do Vigen. </span></span></div>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">Tudo de bom, </span></span></div>
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<span style="font-size:14px;background-color:rgb(255,255,255);display:inline"><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline">---Julio Stern </span></span></div>
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<font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Pedro Alberto Morettin <<a href="mailto:pam@ime.usp.br" target="_blank">pam@ime.usp.br</a>><br>
<b>Sent:</b> Friday, March 5, 2021 3:56 PM<br>
<b>To:</b> Julio Stern <<a href="mailto:jmstern@hotmail.com" target="_blank">jmstern@hotmail.com</a>><br>
<b>Cc:</b> <a href="mailto:abe@lists.ime.usp.br" target="_blank">abe@lists.ime.usp.br</a> <<a href="mailto:abe@lists.ime.usp.br" target="_blank">abe@lists.ime.usp.br</a>><br>
<b>Subject:</b> Re: [ABE-L] Fw: Causalidade X Correlacao</font>
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<div>Julio,</div>
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<div>v. não precisa olhar esses artigos; veja meu livro de Econometria Financeira, Capítulo 10, é mais fácil. As séries que v.</div>
<div>mostrou são (quase) todas não estacionárias. O que Granger e Newbold (1974) mostraram é que, considerando
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<div>duas séries não estacionárias completamente não correlacionadas, a regressão de uma sobre a outra produz produz uma correlação</div>
<div>aparentemente significativa. Daí a necessidade de se desenvolver técnicas (cointegração) para analisar séries não estacionárias integradas</div>
<div>(essas são tais que tomando-se uma ou mais diferenças tornam-se estacionárias).</div>
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<div>Abs,</div>
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<div>Pedro<br>
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<div dir="ltr">Em sex., 5 de mar. de 2021 às 10:03, Julio Stern <<a href="mailto:jmstern@hotmail.com" target="_blank">jmstern@hotmail.com</a>> escreveu:<br>
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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"><br>
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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">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">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"><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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<p style="margin:0in 0in 0.0001pt;line-height:16.8667px;font-size:11pt;font-family:Calibri,sans-serif">
<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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<div dir="ltr"><span style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">Hedibert Freitas Lopes, PhD</span><br style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">
<span style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">Professor of Statistics and Econometrics</span><br style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">
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<span style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">Rua Quatá, 300 - São Paulo, SP 04546-042 Brazil</span><br style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">
<span style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">Phone: +55 11 4504-2343</span><br style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">
<span style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small"><a href="http://www.hedibert.org" target="_blank">www.hedibert.org</a></span><br>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><font face="monospace, monospace"><span style="font-size:12.8px">"</span><span style="color:rgb(84,84,84);font-size:small;line-height:18.2px">If you can't</span><span style="color:rgb(84,84,84);font-size:small;line-height:18.2px"> excel with </span><span style="color:rgb(84,84,84);font-size:small;line-height:18.2px">talent</span><span style="color:rgb(84,84,84);font-size:small;line-height:18.2px">, triumph with </span><span style="color:rgb(84,84,84);font-size:small;line-height:18.2px">effort</span><span style="font-size:12.8px">!" - </span><span style="font-size:12.8px">Dave Weinbaum.</span><br></font></div><div dir="ltr"><font face="monospace, monospace"><br></font></div><div dir="ltr"><font face="monospace, monospace">Widemberg Nobre</font></div><div dir="ltr"><span style="font-size:12.8px"><font face="monospace, monospace">Doutorando em Estatística pela Universidade Federal do Rio de Janeiro</font></span><div><br></div><div><br></div></div></div></div></div></div></div></div></div></div></div></div></div>