<div dir="ltr"><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></div><div>Saudações,<br><br>Diego Samuel Rodrigues</div><div>Faculdade de Tecnologia, Universidade Estadual de Campinas</div><div><br></div><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></div><div><br></div><div><img src="cid:ii_klwqhrrj0" alt="image.png" width="754" height="453" style="margin-right:0px"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">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></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="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-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>
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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: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: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: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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<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"> </span><span style="font-family:Arial,Helvetica,sans-serif;font-size:14pt;display:inline"> </span></span></div>
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<div id="m_3311665484946375010gmail-m_217569403463701082divRplyFwdMsg" dir="ltr"><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
<br>
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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">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">>>>
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<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"><br>
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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>
<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">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"><br>
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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"><br>
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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"><br>
</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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<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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