{"id":877,"date":"2023-07-28T11:11:00","date_gmt":"2023-07-28T11:11:00","guid":{"rendered":"https:\/\/statorials.org\/pt\/autocorrelacao-python\/"},"modified":"2023-07-28T11:11:00","modified_gmt":"2023-07-28T11:11:00","slug":"autocorrelacao-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/autocorrelacao-python\/","title":{"rendered":"Como calcular a autocorrela\u00e7\u00e3o em python"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>A autocorrela\u00e7\u00e3o<\/strong> mede o grau de similaridade entre uma s\u00e9rie temporal e uma vers\u00e3o defasada dela mesma em intervalos de tempo sucessivos.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c0s vezes tamb\u00e9m \u00e9 chamada de \u201ccorrela\u00e7\u00e3o serial\u201d ou \u201ccorrela\u00e7\u00e3o defasada\u201d porque mede a rela\u00e7\u00e3o entre os valores atuais de uma vari\u00e1vel e seus valores hist\u00f3ricos.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Quando a autocorrela\u00e7\u00e3o em uma s\u00e9rie temporal \u00e9 alta, torna-se f\u00e1cil prever valores futuros simplesmente referindo-se a valores passados.<\/span><\/p>\n<h3> <strong>Como calcular a autocorrela\u00e7\u00e3o em Python<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que temos a seguinte s\u00e9rie temporal em Python que mostra o valor de uma determinada vari\u00e1vel para 15 per\u00edodos diferentes:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define data<\/span>\nx = [22, 24, 25, 25, 28, 29, 34, 37, 40, 44, 51, 48, 47, 50, 51]\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Podemos calcular a autocorrela\u00e7\u00e3o para cada atraso na s\u00e9rie temporal usando a <a href=\"https:\/\/www.statsmodels.org\/stable\/generated\/statsmodels.tsa.stattools.acf.html\" target=\"_blank\" rel=\"noopener noreferrer\">fun\u00e7\u00e3o acf()<\/a> da biblioteca statsmodels:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> statsmodels.api <span style=\"color: #107d3f;\">as<\/span> sm\n\n<span style=\"color: #008080;\">#calculate autocorrelations<\/span>\nsm.tsa.acf(x)\n\narray([ 1. , 0.83174224, 0.65632458, 0.49105012, 0.27863962,\n        0.03102625, -0.16527446, -0.30369928, -0.40095465, -0.45823389,\n       -0.45047733])\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A forma de interpretar o resultado \u00e9 a seguinte:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">A autocorrela\u00e7\u00e3o no atraso 0 \u00e9 <strong>1<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">A autocorrela\u00e7\u00e3o no atraso 1 \u00e9 <strong>0,8317<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">A autocorrela\u00e7\u00e3o no atraso 2 \u00e9 <strong>0,6563<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">A autocorrela\u00e7\u00e3o no atraso 3 \u00e9 <strong>0,4910<\/strong> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">E assim por diante.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tamb\u00e9m podemos especificar o n\u00famero de defasagens a serem usadas com o argumento <strong>nlags<\/strong> :<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>sm.tsa.acf(x, nlags= <span style=\"color: #008000;\">5<\/span> )\n\narray([1.0, 0.83174224, 0.65632458, 0.49105012, 0.27863962, 0.03102625])<\/strong><\/pre>\n<h3> <strong>Como tra\u00e7ar a fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o em Python<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Podemos tra\u00e7ar a fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o para uma s\u00e9rie temporal em Python usando a <a href=\"https:\/\/www.statsmodels.org\/dev\/generated\/statsmodels.graphics.tsaplots.plot_acf.html\" target=\"_blank\" rel=\"noopener noreferrer\">fun\u00e7\u00e3o tsaplots.plot_acf()<\/a> da biblioteca statsmodels:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> statsmodels.graphics <span style=\"color: #107d3f;\">import<\/span> tsaplots\n<span style=\"color: #107d3f;\">import<\/span> matplotlib.pyplot <span style=\"color: #107d3f;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#plot autocorrelation function<\/span>\nfig = tsaplots.plot_acf(x, lags=10)\nplt.show()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9480 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/autocorrelationpython1.png\" alt=\"Fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o em Python\" width=\"495\" height=\"343\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">O eixo x exibe o n\u00famero de defasagens e o eixo y exibe a autocorrela\u00e7\u00e3o nesse n\u00famero de defasagens. Por padr\u00e3o, o gr\u00e1fico come\u00e7a em lag = 0 e a autocorrela\u00e7\u00e3o sempre ser\u00e1 <strong>1<\/strong> em lag = 0.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tamb\u00e9m podemos ampliar os primeiros atrasos escolhendo usar menos atrasos com o argumento <strong>lags<\/strong> :<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> statsmodels.graphics <span style=\"color: #107d3f;\">import<\/span> tsaplots\n<span style=\"color: #107d3f;\">import<\/span> matplotlib.pyplot <span style=\"color: #107d3f;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#plot autocorrelation function<\/span>\nfig = tsaplots.plot_acf(x, lags= <span style=\"color: #008000;\">5<\/span> )\nplt.show()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9481 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/autocorrelationpython2.png\" alt=\"Plotando fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o em Python\" width=\"495\" height=\"329\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Voc\u00ea tamb\u00e9m pode alterar o t\u00edtulo e a cor dos c\u00edrculos usados no gr\u00e1fico com os argumentos <strong>t\u00edtulo<\/strong> e <strong>cor<\/strong> :<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> statsmodels.graphics <span style=\"color: #107d3f;\">import<\/span> tsaplots\n<span style=\"color: #107d3f;\">import<\/span> matplotlib.pyplot <span style=\"color: #107d3f;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#plot autocorrelation function<\/span>\nfig = tsaplots.plot_acf(x, lags= <span style=\"color: #008000;\"><span style=\"color: #000000;\">5, color='g', title='Autocorrelation function'<\/span><\/span> <span style=\"color: #000000;\">)<\/span>\nplt.show()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9482 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/autocorrelationpython4.png\" alt=\"Fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o em Python com t\u00edtulo personalizado\" width=\"499\" height=\"342\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><em>Voc\u00ea pode encontrar mais tutoriais de Python <a href=\"https:\/\/statorials.org\/pt\/estatologia-explica-conceitos-de-forma-simples-e-direta-facilitamos-o-aprendizado-de-estatistica\/\" target=\"_blank\" rel=\"noopener noreferrer\">nesta p\u00e1gina<\/a> .<\/em><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A autocorrela\u00e7\u00e3o mede o grau de similaridade entre uma s\u00e9rie temporal e uma vers\u00e3o defasada dela mesma em intervalos de tempo sucessivos. \u00c0s vezes tamb\u00e9m \u00e9 chamada de \u201ccorrela\u00e7\u00e3o serial\u201d ou \u201ccorrela\u00e7\u00e3o defasada\u201d porque mede a rela\u00e7\u00e3o entre os valores atuais de uma vari\u00e1vel e seus valores hist\u00f3ricos. Quando a autocorrela\u00e7\u00e3o em uma s\u00e9rie temporal [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-877","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como calcular a autocorrela\u00e7\u00e3o em Python - Estatologia<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples sobre como calcular e tra\u00e7ar uma fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o em Python.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pt\/autocorrelacao-python\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como calcular a autocorrela\u00e7\u00e3o em Python - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples sobre como calcular e tra\u00e7ar uma fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o em Python.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/autocorrelacao-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T11:11:00+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/autocorrelationpython1.png\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/autocorrelacao-python\/\",\"url\":\"https:\/\/statorials.org\/pt\/autocorrelacao-python\/\",\"name\":\"Como calcular a autocorrela\u00e7\u00e3o em Python - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T11:11:00+00:00\",\"dateModified\":\"2023-07-28T11:11:00+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples sobre como calcular e tra\u00e7ar uma fun\u00e7\u00e3o de autocorrela\u00e7\u00e3o em Python.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/autocorrelacao-python\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/autocorrelacao-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/autocorrelacao-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como calcular a autocorrela\u00e7\u00e3o em python\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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