{"id":1475,"date":"2022-10-11T13:30:08","date_gmt":"2022-10-11T13:30:08","guid":{"rendered":"https:\/\/sbia.org.br\/lnlm\/?page_id=1475"},"modified":"2022-10-22T18:21:15","modified_gmt":"2022-10-22T18:21:15","slug":"vol20-no1-art4","status":"publish","type":"page","link":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/","title":{"rendered":"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction"},"content":{"rendered":"<p>J\u00f4natas T. Belotti <a href=\"https:\/\/orcid.org\/0000-0002-1483-2321\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Jos\u00e9 J. A. Mendes Junior <a href=\"https:\/\/orcid.org\/0000-0001-5578-7734\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Ivette Luna <a href=\"https:\/\/orcid.org\/0000-0002-5304-5523\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Patr\u00edcia T. Leite Asano <a href=\"https:\/\/orcid.org\/0000-0003-2410-3621\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Yara de Souza Tadano <a href=\"https:\/\/orcid.org\/0000-0002-3975-3419\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Thiago Antonini Alves <a href=\"https:\/\/orcid.org\/0000-0003-2950-7377\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Marcella S. R. Martins <a href=\"https:\/\/orcid.org\/0000-0002-5716-4968\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>F\u00e1bio L. Usberti <a href=\"https:\/\/orcid.org\/0000-0002-8972-080X\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Sergio L. Stevan Jr <a href=\"https:\/\/orcid.org\/0000-0002-4783-5350\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>Fl\u00e1vio Trojan <a href=\"https:\/\/orcid.org\/0000-0003-2274-5321\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>&amp; Hugo Siqueira <a href=\"https:\/\/orcid.org\/0000-0002-1278-4602\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a><\/p>\n<p><strong>Abstract:<\/strong> Linear models are widely used to perform time series forecasting. The Autoregressive models stand out, due to their simplicity in the parameters adjustment based on close-form solution. The Autoregressive and Moving Average models (ARMA) and Infinite Impulse Response filters (IIR) are also good alternatives, since they are recurrent structures. However, their adjustment is more complex, since the problem has no analytical solution. This investigation performs linear models to predict monthly seasonal streamflow series, from to Brazilian hydroelectric plants. The goal is to reach the best achievable performance addressing linear approaches. We propose the application of recurrent models, estimating their parameters via an immune algorithm. To compare the optimization performance, the Least Mean Square (LMS) and Recursive Prediction Error (RPE) algorithms are utilized. Also, the AR model and the Holt-Winters method were performed. The results showed that the insertion of feedback loops increases the quality of the responses. The ARMA models optimized by the immune algorithms achieved the best overall performance.<\/p>\n<p><strong>Keywords:<\/strong> Seasonal streamflow series forecasting, Box &amp; Jenkins Models, IIR filters, immune algorithm.<\/p>\n<p><strong>DOI code:<\/strong> <a href=\"http:\/\/dx.doi.org\/10.21528\/lnlm-vol20-no1-art4\">10.21528\/lnlm-vol20-no1-art4<\/a><\/p>\n<p><strong>PDF file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2022\/12\/vol20-no1-art4.pdf\">vol20-no1-art4.pdf<\/a><\/p>\n<p><strong>BibTex file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2022\/12\/vol20-no1-art4.bib\">vol20-no1-art4.bib<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>J\u00f4natas T. Belotti Jos\u00e9 J. A. Mendes Junior Ivette Luna Patr\u00edcia T. Leite Asano Yara de Souza Tadano Thiago Antonini Alves Marcella S. R. Martins F\u00e1bio L. Usberti Sergio L. Stevan Jr Fl\u00e1vio Trojan &amp; Hugo Siqueira Abstract: Linear models <a href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1458,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1475","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Linear Models Applied to Monthly Seasonal Streamflow Series Prediction - Learning and NonLinear Models<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction - Learning and NonLinear Models\" \/>\n<meta property=\"og:description\" content=\"J\u00f4natas T. Belotti Jos\u00e9 J. A. Mendes Junior Ivette Luna Patr\u00edcia T. Leite Asano Yara de Souza Tadano Thiago Antonini Alves Marcella S. R. Martins F\u00e1bio L. Usberti Sergio L. Stevan Jr Fl\u00e1vio Trojan &amp; Hugo Siqueira Abstract: Linear models Read More ...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/\" \/>\n<meta property=\"og:site_name\" content=\"Learning and NonLinear Models\" \/>\n<meta property=\"article:modified_time\" content=\"2022-10-22T18:21:15+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/\",\"name\":\"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction - Learning and NonLinear Models\",\"isPartOf\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\",\"datePublished\":\"2022-10-11T13:30:08+00:00\",\"dateModified\":\"2022-10-22T18:21:15+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#primaryimage\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\",\"contentUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Browse issues\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Learning &#038; Nonlinear Models &#8211; L&#038;NLM &#8211; Volume 20 &#8211; N\u00famero 1\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"name\":\"Learning and NonLinear Models\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sbia.org.br\/lnlm\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\",\"name\":\"Learning and NonLinear Models\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"contentUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"width\":398,\"height\":94,\"caption\":\"Learning and NonLinear Models\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction - Learning and NonLinear Models","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/","og_locale":"pt_BR","og_type":"article","og_title":"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction - Learning and NonLinear Models","og_description":"J\u00f4natas T. Belotti Jos\u00e9 J. A. Mendes Junior Ivette Luna Patr\u00edcia T. Leite Asano Yara de Souza Tadano Thiago Antonini Alves Marcella S. R. Martins F\u00e1bio L. Usberti Sergio L. Stevan Jr Fl\u00e1vio Trojan &amp; Hugo Siqueira Abstract: Linear models Read More ...","og_url":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/","og_site_name":"Learning and NonLinear Models","article_modified_time":"2022-10-22T18:21:15+00:00","og_image":[{"url":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg","type":"","width":"","height":""}],"twitter_card":"summary_large_image","twitter_misc":{"Est. tempo de leitura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/","url":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/","name":"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction - Learning and NonLinear Models","isPartOf":{"@id":"https:\/\/sbia.org.br\/lnlm\/#website"},"primaryImageOfPage":{"@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#primaryimage"},"image":{"@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#primaryimage"},"thumbnailUrl":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg","datePublished":"2022-10-11T13:30:08+00:00","dateModified":"2022-10-22T18:21:15+00:00","breadcrumb":{"@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/"]}]},{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#primaryimage","url":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg","contentUrl":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/vol20-no1-art4\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Browse issues","item":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/"},{"@type":"ListItem","position":2,"name":"Learning &#038; Nonlinear Models &#8211; L&#038;NLM &#8211; Volume 20 &#8211; N\u00famero 1","item":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol20-no1\/"},{"@type":"ListItem","position":3,"name":"Linear Models Applied to Monthly Seasonal Streamflow Series Prediction"}]},{"@type":"WebSite","@id":"https:\/\/sbia.org.br\/lnlm\/#website","url":"https:\/\/sbia.org.br\/lnlm\/","name":"Learning and NonLinear Models","description":"","publisher":{"@id":"https:\/\/sbia.org.br\/lnlm\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sbia.org.br\/lnlm\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/sbia.org.br\/lnlm\/#organization","name":"Learning and NonLinear Models","url":"https:\/\/sbia.org.br\/lnlm\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/","url":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png","contentUrl":"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png","width":398,"height":94,"caption":"Learning and NonLinear Models"},"image":{"@id":"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages\/1475","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/comments?post=1475"}],"version-history":[{"count":5,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages\/1475\/revisions"}],"predecessor-version":[{"id":1495,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages\/1475\/revisions\/1495"}],"up":[{"embeddable":true,"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/pages\/1458"}],"wp:attachment":[{"href":"https:\/\/sbia.org.br\/lnlm\/wp-json\/wp\/v2\/media?parent=1475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}