{"id":2750,"date":"2015-03-13T21:37:48","date_gmt":"2015-03-14T00:37:48","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=2750"},"modified":"2025-09-16T16:18:12","modified_gmt":"2025-09-16T19:18:12","slug":"series-temporais","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/","title":{"rendered":"Estat\u00edstica"},"content":{"rendered":"<p style=\"text-align: right;\"><strong><em><span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\">&#8220;A Estat\u00edstica \u00e9 a \u00fanica ci\u00eancia que permite dois especialistas tirarem conclus\u00f5es diferentes a partir dos mesmos dados&#8221;<\/span><\/em><\/strong><\/p>\n<p style=\"text-align: right;\"><em><span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\">Evan Esar, humorista americano<\/span><\/em><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">A Estat\u00edstica possui papel de destaque na gera\u00e7\u00e3o de energia el\u00e9trica porque fornece as melhores ferramentas para extrair informa\u00e7\u00e3o de grandes volumes de dados.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">A demanda de energia, a \u00e1gua nas hidrel\u00e9tricas, o sol na gera\u00e7\u00e3o solar, os ventos na gera\u00e7\u00e3o e\u00f3lica e o pre\u00e7o dos combust\u00edveis apresentam comportamentos rand\u00f4micos e a estat\u00edstica, deixando o humor de lado, permanece como a melhor ferramenta para estud\u00e1-los.<\/span><\/p>\n<h2 id='espa\u00e7o-de-amostragem'  id=\"boomdevs_1\" style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Espa\u00e7o de Amostragem<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><strong><em>Espa\u00e7o de amostragem<\/em><\/strong> \u2013 <strong>S<\/strong> &#8211; ou <strong>Popula\u00e7\u00e3o<\/strong> consiste no conjunto de todos os poss\u00edveis valores das grandezas aleat\u00f3rias estudadas. Mais precisamente, o conjunto de todos os poss\u00edveis eventos simples ou elementares constitui o espa\u00e7o de amostragem. Por exemplo, o conjunto de todas as poss\u00edveis vaz\u00f5es de determinado ponto de um rio representa um espa\u00e7o de amostragem. Isto nos leva \u00e0s seguintes quest\u00f5es pr\u00e1ticas:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u00c9 poss\u00edvel quantificar o espa\u00e7o de amostragem?<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u00c9 poss\u00edvel determinar seus valores m\u00e1ximo e m\u00ednimo?<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u00c9 poss\u00edvel prever seu comportamento?<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Os espa\u00e7os de amostragem podem ser <strong>finitos ou infinitos<\/strong> dependendo da grandeza estudada. <strong>Espa\u00e7os Finitos<\/strong> possuem uma quantidade finita de elementos, e <strong>Espa\u00e7os Infinitos<\/strong> possuem uma quantidade infinita de elementos. Por exemplo, a vaz\u00e3o de um rio possui Espa\u00e7o Infinito porque pode variar continuamente entre zero e infinito, mas o n\u00famero de turbinas em opera\u00e7\u00e3o possui Espa\u00e7o Finito porque varia discretamente entre zero e o n\u00famero de m\u00e1quinas instaladas.<\/span><\/p>\n<h2 id='evento'  id=\"boomdevs_2\" style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Evento<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>Evento<\/strong> representa um subconjunto <strong>A<\/strong> do espa\u00e7o de amostragem <strong>S<\/strong>. Eventos podem ser <strong>Simples <\/strong>ou <strong>Compostos<\/strong>. Denomina-se <strong>Evento Elementar<\/strong> ou <strong>Simples<\/strong> um subconjunto unit\u00e1rio do Espa\u00e7o de Amostragem. Por outro lado, conjuntos formados por diversos elementos simples formam os <strong>Eventos Compostos<\/strong>. Por exemplo, cada velocidade de vento medida representa um Evento Simples, e o conjunto de vaz\u00f5es semanais de um rio constitui um Evento Composto.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Considere os pontos coloridos na Figura 1 como Eventos Simples de um mesmo espa\u00e7o de amostragem (o alvo). A necessidade de medir a localiza\u00e7\u00e3o e o espalhamento destes eventos surge naturalmente. Intuitivamente, apesar de nenhum dos eventos ter acertado o centro do alvo, o centro representa a medida de localiza\u00e7\u00e3o de todos os eventos. Por outro lado, a dist\u00e2ncia dos pontos ao centro mede o espalhamento dos eventos. Outros par\u00e2metros poderiam ser criados para medir a localiza\u00e7\u00e3o e o espalhamento.<\/span><\/p>\n<figure id=\"attachment_22293\" aria-describedby=\"caption-attachment-22293\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/media.png\" rel=\"attachment wp-att-5282\"><img decoding=\"async\" class=\"wp-image-22293 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/media.png\" alt=\"\" width=\"600\" height=\"500\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/media.png 600w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/media-300x250.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/a><figcaption id=\"caption-attachment-22293\" class=\"wp-caption-text\">Figura 1. Eventos<\/figcaption><\/figure>\n<h2 id='probabilidade'  id=\"boomdevs_3\" style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">Probabilidade<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No caso de <strong><em>Espa\u00e7os de Amostragem<\/em> Finitos<\/strong>, define-se a probabilidade <strong>P(A)<\/strong> como <strong>h\/n<\/strong>, onde <strong>h<\/strong> \u00e9 o n\u00famero de ocorr\u00eancias do evento A e <strong>n<\/strong> o n\u00famero de Eventos Simples do Espa\u00e7o Amostral. Por exemplo, a probabilidade de um determinado n\u00famero sorteado na Megasena \u00e9 igual a 1\/60.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No entanto, qual a probabilidade de a vaz\u00e3o de uma usina hidrel\u00e9trica ser inferior \u00e0 m\u00ednima registrada nos \u00faltimos 80 anos? Para responder a esta pergunta necessitamos definir probabilidade em Espa\u00e7os de Amostragem Infinitos. Neste caso, define-se probabilidade da seguinte maneira:<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">De acordo com Spiegel,<em> &#8220;Se ap\u00f3s n repeti\u00e7\u00f5es de um experimento, sendo n um n\u00famero suficientemente grande, um determinado Evento A ocorreu h vezes, define-se a probabilidade do Evento A da seguinte maneira: P(A)=h\/n.&#8221;[1]<\/em><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O problema desta defini\u00e7\u00e3o reside em determinar o conceito de &#8220;grande o suficiente&#8221; para garantir a converg\u00eancia da probabilidade e, dado um n finito, qual o erro cometido. Na pr\u00e1tica, quanto maior o n\u00famero de dados medidos menor ser\u00e1 o erro.<\/span><\/p>\n<h3 id='axiomas'  id=\"boomdevs_4\"><span style=\"font-family: verdana, geneva, sans-serif;\">Axiomas<\/span><\/h3>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A probabilidade \u00e9 sempre positiva.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A probabilidade \u00e9 sempre menor ou igual a 1.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A probabilidade de um evento \u00e9 1 quando o evento sempre ocorre.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A probabilidade de um evento \u00e9 zero quando jamais ocorre.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Se o Evento A\u2019 \u00e9 o complemento de A, ent\u00e3o <strong>P(A\u2019) = 1-P(A)<\/strong><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Somat\u00f3rio ou integral das probabilidades de todos os Eventos Simples de um espa\u00e7o S \u00e9 sempre igual a 1.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Para quaisquer dois eventos A e B, a probabilidade da uni\u00e3o dos dois eventos corresponde a soma das probabilidades dos eventos menos a probabilidade de os eventos ocorrerem simultaneamente. Se eles forem mutuamente excludentes, a probabilidade da uni\u00e3o \u00e9 a soma das probabilidades individuais.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<figure id=\"attachment_22290\" aria-describedby=\"caption-attachment-22290\" style=\"width: 518px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/Prob_uniao.png\"><img decoding=\"async\" class=\"wp-image-22290\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/Prob_uniao.png\" alt=\"\" width=\"518\" height=\"40\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/Prob_uniao.png 661w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/Prob_uniao-300x23.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/a><figcaption id=\"caption-attachment-22290\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 1. Probabilidade da uni\u00e3o<\/figcaption><\/figure>\n<figure id=\"attachment_5118\" aria-describedby=\"caption-attachment-5118\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/Minhas-Notas-Page-7-e1454274627864.png\" rel=\"attachment wp-att-5118\"><img decoding=\"async\" class=\"wp-image-5118\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/Minhas-Notas-Page-7-e1454274627864-1024x768.png\" alt=\"Minhas Notas - Page 7\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/Minhas-Notas-Page-7-e1454274627864.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/Minhas-Notas-Page-7-e1454274627864-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/Minhas-Notas-Page-7-e1454274627864-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-5118\" class=\"wp-caption-text\">Figura 2. Uni\u00e3o de Eventos<\/figcaption><\/figure>\n<h3 id='probabilidade-condicional'  id=\"boomdevs_5\"><span style=\"font-family: verdana, geneva, sans-serif;\">Probabilidade Condicional<\/span><\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Sejam A e B dois eventos de um espa\u00e7o S com probabilidades maiores que zero. A Equa\u00e7\u00e3o 2 determina a probabilidade de A ocorrer dado que B tamb\u00e9m ocorre.<\/span><\/p>\n<figure id=\"attachment_39990\" aria-describedby=\"caption-attachment-39990\" style=\"width: 387px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/03\/prob_cond.png\"><img decoding=\"async\" class=\"wp-image-39990 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/03\/prob_cond.png\" alt=\"\" width=\"387\" height=\"99\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/03\/prob_cond.png 387w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2021\/03\/prob_cond-300x77.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/a><figcaption id=\"caption-attachment-39990\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 2. Probabilidade Condicional<\/figcaption><\/figure>\n<h2 id='distribui\u00e7\u00e3o-de-probabilidade'  id=\"boomdevs_6\" align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Distribui\u00e7\u00e3o de Probabilidade<\/span><\/h2>\n<p align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">Se associarmos um n\u00famero x a cada ponto de um espa\u00e7o de amostragem a <strong>Fun\u00e7\u00e3o Probabilidade ou Distribui\u00e7\u00e3o de Probabilidade &#8211; <em>f<\/em>(<em>x<\/em>) <\/strong>ser\u00e1 igual a probabilidade de x. Se o espa\u00e7o de amostragem for finito as vari\u00e1veis rand\u00f4micas ou estoc\u00e1sticas ser\u00e3o discretas. Caso contr\u00e1rio, as vari\u00e1veis s\u00e3o cont\u00ednuas.<\/span><\/p>\n<figure id=\"attachment_22297\" aria-describedby=\"caption-attachment-22297\" style=\"width: 317px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_prob_1.png\"><img decoding=\"async\" class=\"wp-image-22297 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_prob_1.png\" alt=\"\" width=\"317\" height=\"198\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_prob_1.png 317w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_prob_1-300x187.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/a><figcaption id=\"caption-attachment-22297\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 3. Distribui\u00e7\u00e3o de Probabilidade<\/figcaption><\/figure>\n<h2 id='distribui\u00e7\u00e3o-acumulada'  id=\"boomdevs_7\" align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Distribui\u00e7\u00e3o Acumulada<\/span><\/h2>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">A <strong>Fun\u00e7\u00e3o de Distribui\u00e7\u00e3o Acumulada<\/strong> \u00e9 a soma ou a integral da distribui\u00e7\u00e3o de probabilidade entre 0 e o ponto x.<\/span><\/p>\n<figure id=\"attachment_22298\" aria-describedby=\"caption-attachment-22298\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_acu.png\"><img decoding=\"async\" class=\"wp-image-22298 size-medium\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_acu-300x264.png\" alt=\"\" width=\"300\" height=\"264\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_acu-300x264.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/dist_acu.png 319w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-22298\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 4. Distribui\u00e7\u00e3o acumulada<\/figcaption><\/figure>\n<h2 id='valor-esperado-e-m\u00e9dia'  id=\"boomdevs_8\" align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Valor Esperado e M\u00e9dia<\/span><\/h2>\n<p align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">O <strong>Valor Esperado &#8211; E(x) &#8211;<\/strong> de uma vari\u00e1vel aleat\u00f3ria x constitui um dos conceitos mais importantes da estat\u00edstica. Ele representa o valor esperado ou mais prov\u00e1vel de uma vari\u00e1vel aleat\u00f3ria. Calcula-se o valor esperado de determinada vari\u00e1vel aleat\u00f3ria <em>x<\/em> de acordo com a equa\u00e7\u00e3o 5.<\/span><\/p>\n<figure id=\"attachment_22299\" aria-describedby=\"caption-attachment-22299\" style=\"width: 359px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_esperado.png\"><img decoding=\"async\" class=\"wp-image-22299 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_esperado.png\" alt=\"\" width=\"359\" height=\"112\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_esperado.png 359w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_esperado-300x94.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/a><figcaption id=\"caption-attachment-22299\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 5. Valor Esperado<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No caso particular de as probabilidades serem iguais, o valor esperado equivale \u00e0 m\u00e9dia aritm\u00e9tica. <span id='easy-footnote-1-2750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/#easy-footnote-bottom-1-2750' title=' demonstre isto'><sup>1<\/sup><\/a><\/span><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A rigor, o <strong>valor esperado<\/strong> se encontra associado a <strong>eventos<\/strong> ou amostras de determinado espa\u00e7o amostral enquanto a <strong>m\u00e9dia estat\u00edstica<\/strong> &#8211; <strong>\u03bc &#8211; <\/strong>representa os dados de toda a popula\u00e7\u00e3o ou quando a fun\u00e7\u00e3o de distribui\u00e7\u00e3o de probabilidade \u00e9 conhecida. Por\u00e9m, na pr\u00e1tica esta distin\u00e7\u00e3o nem sempre se encontra bem definida e utilizam-se os termos valor esperado e m\u00e9dia algumas vezes de forma incorreta.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Deve-se ressaltar que a <strong>m\u00e9dia estat\u00edstica<\/strong> s\u00f3 se iguala \u00e0 <strong>m\u00e9dia aritm\u00e9tica<\/strong> quando todos os eventos possuem a mesma probabilidade de ocorrer. A m\u00e9dia estat\u00edstica consiste no conceito estat\u00edstico mais utilizado na pr\u00e1tica e pertence ao grupo de medidas de localiza\u00e7\u00e3o.<\/span><\/p>\n<h5 id='teoremas-sobre-valor-esperado'  id=\"boomdevs_9\"><span style=\"font-family: verdana, geneva, sans-serif;\">Teoremas Sobre Valor Esperado<\/span><\/h5>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O valor esperado \u00e9 uma fun\u00e7\u00e3o linear.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">O valor esperado de amostras de uma popula\u00e7\u00e3o \u00e9 a m\u00e9dia da popula\u00e7\u00e3o.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<figure id=\"attachment_22302\" aria-describedby=\"caption-attachment-22302\" style=\"width: 438px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_espe_linear.png\"><img decoding=\"async\" class=\"wp-image-22302 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_espe_linear.png\" alt=\"\" width=\"438\" height=\"99\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_espe_linear.png 438w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/valor_espe_linear-300x68.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/a><figcaption id=\"caption-attachment-22302\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 6. Linearidade do valor esperado<\/figcaption><\/figure>\n<h2 id='moda'  id=\"boomdevs_10\"><span style=\"font-family: verdana, geneva, sans-serif;\">Moda<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Moda de uma vari\u00e1vel rand\u00f4mica representa o valor que ocorre com maior frequ\u00eancia ou com maior probabilidade. Quando isto ocorre, <strong>a derivada da fun\u00e7\u00e3o probabilidade \u00e9 igual a zero<\/strong>. Existem vari\u00e1veis rand\u00f4micas com mais de uma moda. Neste caso, denominam-se de bimodal ou multimodal. A Moda tamb\u00e9m representa uma vari\u00e1vel de localiza\u00e7\u00e3o.<\/span><\/p>\n<h2 id='mediana'  id=\"boomdevs_11\"><span style=\"font-family: verdana, geneva, sans-serif;\">Mediana<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A mediana \u00e9 o valor da vari\u00e1vel rand\u00f4mica que separa a fun\u00e7\u00e3o de distribui\u00e7\u00e3o acumulada em duas metades, possui o valor de probabilidade de 50% e equivale ao percentil de 50%. A mediana e m\u00e9dia nem sempre se igualam. A mediana, m\u00e9dia, e moda se igualam apenas em distribui\u00e7\u00f5es de probabilidade sim\u00e9tricas, como no caso da distribui\u00e7\u00e3o normal ou gaussiana.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A mediana \u00e9 a medida mais <strong>robusta<\/strong> e <strong>resistente<\/strong> da tend\u00eancia central de uma vari\u00e1vel aleat\u00f3ria e servindo tamb\u00e9m como medida de localiza\u00e7\u00e3o.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Medidas robustas n\u00e3o fornecem a solu\u00e7\u00e3o \u00f3tima para problemas espec\u00edficos, mas produzem resultados satisfat\u00f3rios para a maioria dos problemas. Medidas robustas s\u00e3o normalmente insens\u00edveis a pressupostos sobre as caracter\u00edsticas das vari\u00e1veis. Por exemplo, a m\u00e9dia \u00e9 a melhor medida do centro de uma vari\u00e1vel aleat\u00f3ria se ela tiver um comportamento sim\u00e9trico. Por isso, a m\u00e9dia n\u00e3o \u00e9 uma medida robusta. Por outro lado, medidas resistentes s\u00e3o insens\u00edveis a &#8220;pontos fora da curva&#8221; ou grandes varia\u00e7\u00f5es de poucos pontos. A m\u00e9dia tamb\u00e9m \u00e9 mais sens\u00edvel do que a mediana a valores fora da curva.\u00a0<\/span><\/p>\n<h2 id='momento-de-ordem-r'  id=\"boomdevs_12\" align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Momento de Ordem r<\/span><\/h2>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Apenas o valor esperado n\u00e3o caracteriza uma vari\u00e1vel aleat\u00f3ria. Duas vari\u00e1veis podem ter a mesma m\u00e9dia, mas ter distribui\u00e7\u00f5es de probabilidade diferentes, conforme mostra a Figura 3. A m\u00e9dia das duas vari\u00e1veis \u00e9 zero, mas a vari\u00e1vel #2 est\u00e1 menos concentrada do que a vari\u00e1vel #1.<\/span><\/p>\n<p style=\"text-align: center;\" align=\"left\">\n<div class=\"wdt-wrapper-chart-loader\" data-id=\"128\"\n     style=\"height: 600px;\">\n    <div class=\"wdt-main-item\">\n                <div class=\"wdt-chart-animated-background\" style=\"height: 150px\">\n            <div class=\"wdt-background-masker wdt-btn-divide-left wdt-chart-one\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-2\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-3\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-4 wdt-chart-three\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-5\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-6\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-7 \"><\/div>\n         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wdt-btn-divide-left-4\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-5\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-6\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-7\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-8\"><\/div>\n        <\/div>\n        <div class=\"wdt-static-background\">\n            <div class=\"wdt-background-masker\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n<style>\n    \n<\/style>    <script type=\"text\/javascript\">\n        if (typeof (wpDataCharts) == 'undefined') wpDataCharts = {};\n        wpDataCharts[128] = {\n            render_data: {\"columns\":[{\"type\":\"number\",\"label\":\"x\",\"orig_header\":\"x\"},{\"type\":\"number\",\"label\":\"Desvio = 1\",\"orig_header\":\"desvio1\"},{\"type\":\"number\",\"label\":\"Desvio = 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2\",\"color\":\"#DC3912\",\"orig_header\":\"desvio2\"}],\"group_chart\":false,\"loader\":true,\"chartLoaderColorSettings\":\"\",\"chartLoaderAnimationColorSettings\":\"\",\"show_grid\":true,\"type\":\"google_line_chart\"},\n            engine: \"google\",\n            type: \"google_line_chart\",\n            title: \"Distribui\u00e7\u00e3o Probabilidade\",\n            container: \"wpDataChart_128\",\n            follow_filtering: 0,\n            wpdatatable_id: 175,\n            group_chart: 0        }\n    <\/script>\n\n    <div id=\"wpDataChart_128\" class=\"google_line_chart\" style=\"width: 100%\"><\/div>\n<\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 12pt; font-family: verdana, geneva, sans-serif;\">Figura 3. Distribui\u00e7\u00e3o de Probabilidade de dados com a mesma m\u00e9dia<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, a caracteriza\u00e7\u00e3o de vari\u00e1veis aleat\u00f3rias requer outros par\u00e2metros.<\/span><\/p>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Define-se o <strong>Momento de ordem r<\/strong> de uma vari\u00e1vel aleat\u00f3ria X como:<\/span><\/p>\n<figure id=\"attachment_2782\" aria-describedby=\"caption-attachment-2782\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r.png\"><img decoding=\"async\" class=\"wp-image-2782 size-medium\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r-300x117.png\" alt=\"Momento de ordem r\" width=\"300\" height=\"117\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r-300x117.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r.png 381w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-2782\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 7. Momento de ordem r<\/span><\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">M<sup>r<\/sup> \u00e9 o momento de ordem r;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">r \u00e9 a ordem;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">x<sub>i<\/sub> \u00e9 a vari\u00e1vel aleat\u00f3ria;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">N \u00e9 o n\u00famero de vari\u00e1veis na amostra.<\/span><\/li>\n<\/ul>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se que o <strong>momento de ordem 1<\/strong> representa a <strong>m\u00e9dia aritm\u00e9tica<\/strong> da vari\u00e1vel aleat\u00f3ria.<\/span><\/p>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Define-se o <strong>momento de ordem r ao redor da m\u00e9dia<\/strong> da seguinte maneira:<\/span><\/p>\n<figure id=\"attachment_2783\" aria-describedby=\"caption-attachment-2783\" style=\"width: 450px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r_2.png\"><img decoding=\"async\" class=\"wp-image-2783\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r_2.png\" alt=\"Momento ao redor da m\u00e9dia\" width=\"450\" height=\"129\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r_2.png 532w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/momento_r_2-300x86.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/a><figcaption id=\"caption-attachment-2783\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 8. Momento ao redor da m\u00e9dia<\/span><\/figcaption><\/figure>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">O momento ao redor da m\u00e9dia de ordem 1 \u00e9 zero.\u00a0<\/span><\/p>\n<h2 id='vari\u00e2ncia-e-desvio-padr\u00e3o'  id=\"boomdevs_13\" align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Vari\u00e2ncia e Desvio Padr\u00e3o<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana, geneva, sans-serif;\">O <strong>momento de segunda ordem centrado na m\u00e9dia<\/strong> <strong>&#8211; \u03bc<sub>2<\/sub><\/strong>&#8211; consiste no primeiro momento diferente de zero e se tornou conhecido como <strong>vari\u00e2ncia.<\/strong> Como a vari\u00e2ncia possui dimens\u00e3o igual ao quadrado da dimens\u00e3o da vari\u00e1vel aleat\u00f3ria, perde-se o sentimento da unidade deste n\u00famero. Para fugir deste inconveniente, define-se o <strong>desvio padr\u00e3o<\/strong> &#8211; <strong>\u03c3<\/strong> &#8211; como a raiz quadrada da vari\u00e2ncia. Desta forma, o desvio padr\u00e3o possui a mesma dimens\u00e3o da vari\u00e1vel aleat\u00f3ria em quest\u00e3o.<\/span><\/p>\n<figure id=\"attachment_22307\" aria-describedby=\"caption-attachment-22307\" style=\"width: 558px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/variancia.png\"><img decoding=\"async\" class=\"wp-image-22307 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/variancia.png\" alt=\"\" width=\"558\" height=\"229\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/variancia.png 558w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/variancia-300x123.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/a><figcaption id=\"caption-attachment-22307\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 9. Vari\u00e2ncia e Desvio Padr\u00e3o<\/figcaption><\/figure>\n<h2 id='covari\u00e2ncia'  id=\"boomdevs_14\"><span style=\"font-family: verdana, geneva, sans-serif;\">Covari\u00e2ncia<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Define-se a covari\u00e2ncia &#8211; \u03c3<sub>xy<\/sub> &#8211; entre duas vari\u00e1veis aleat\u00f3rias X e Y como o valor esperado entre os erros das duas vari\u00e1veis.<\/span><\/p>\n<figure id=\"attachment_22309\" aria-describedby=\"caption-attachment-22309\" style=\"width: 452px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/covariancia.png\"><img decoding=\"async\" class=\"wp-image-22309 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/covariancia.png\" alt=\"\" width=\"452\" height=\"256\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/covariancia.png 452w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/covariancia-300x170.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/a><figcaption id=\"caption-attachment-22309\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 10. Covari\u00e2ncia<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A covari\u00e2ncia possui a dimens\u00e3o do produto das dimens\u00f5es das vari\u00e1veis aleat\u00f3rias.<\/span><\/p>\n<h2 id='correla\u00e7\u00e3o'  id=\"boomdevs_15\"><span style=\"font-family: verdana, geneva, sans-serif;\">Correla\u00e7\u00e3o<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Para fugir do problema da dimens\u00e3o da covari\u00e2ncia, define-se a <strong>correla\u00e7\u00e3o<\/strong> &#8211;\u00a0<strong>\u03c1<\/strong> &#8211; entre duas vari\u00e1veis aleat\u00f3rias X e Y como sendo a covari\u00e2ncia normalizada pelo produto dos desvios das vari\u00e1veis. Deve-se tomar cuidado com a interpreta\u00e7\u00e3o da correla\u00e7\u00e3o porque ela mede a correla\u00e7\u00e3o linear entre as vari\u00e1veis, mas n\u00e3o identifica correla\u00e7\u00f5es n\u00e3o lineares. <span id='easy-footnote-2-2750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/#easy-footnote-bottom-2-2750' title='calcule a correla\u00e7\u00e3o y=x e y=x&lt;sup&gt;2 &lt;\/sup&gt;'><sup>2<\/sup><\/a><\/span><\/span><\/p>\n<figure id=\"attachment_22310\" aria-describedby=\"caption-attachment-22310\" style=\"width: 200px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/correlacao.png\"><img decoding=\"async\" class=\"wp-image-22310 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/correlacao.png\" alt=\"\" width=\"200\" height=\"90\" \/><\/a><figcaption id=\"caption-attachment-22310\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 11. Correla\u00e7\u00e3o<\/figcaption><\/figure>\n<h3 id='teoremas-sobre-vari\u00e2ncia'  id=\"boomdevs_16\"><span style=\"font-family: verdana, geneva, sans-serif;\">Teoremas Sobre Vari\u00e2ncia<\/span><\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Como a Vari\u00e2ncia n\u00e3o \u00e9 uma fun\u00e7\u00e3o linear, torna-se importante analisar algumas de suas propriedades. A Vari\u00e2ncia do produto de uma vari\u00e1vel estoc\u00e1stica X por uma constante c resulta em:<\/span><\/p>\n<figure id=\"attachment_22312\" aria-describedby=\"caption-attachment-22312\" style=\"width: 420px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/VarcX.png\"><img decoding=\"async\" class=\"size-full wp-image-22312\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/VarcX.png\" alt=\"\" width=\"420\" height=\"53\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/VarcX.png 420w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/VarcX-300x38.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/a><figcaption id=\"caption-attachment-22312\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 12. Vari\u00e2ncia do produto de uma constante<\/figcaption><\/figure>\n<p style=\"text-align: left;\" align=\"center\"><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, a Equa\u00e7\u00e3o 13 fornece o valor da<\/span><span style=\"font-family: verdana, geneva, sans-serif;\"> vari\u00e2ncia da soma\/subtra\u00e7\u00e3o de duas vari\u00e1veis aleat\u00f3rias.<\/span><span style=\"font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/var_soma.png\"><img decoding=\"async\" class=\"aligncenter wp-image-4156\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/var_soma.png\" alt=\"var_soma\" width=\"800\" height=\"47\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/var_soma.png 1098w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/var_soma-300x18.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/var_soma-1024x61.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/var_soma-624x37.png 624w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><\/span><\/p>\n<figure id=\"attachment_22315\" aria-describedby=\"caption-attachment-22315\" style=\"width: 821px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/var_da_soma_2.png\"><img decoding=\"async\" class=\"wp-image-22315 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/var_da_soma_2.png\" alt=\"\" width=\"821\" height=\"53\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/var_da_soma_2.png 821w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/var_da_soma_2-300x19.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/var_da_soma_2-768x50.png 768w\" sizes=\"(max-width: 821px) 100vw, 821px\" \/><\/a><figcaption id=\"caption-attachment-22315\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 13. Vari\u00e2ncia da soma de vari\u00e1veis estoc\u00e1sticas<\/figcaption><\/figure>\n<p style=\"text-align: justify;\" align=\"center\"><span style=\"font-family: verdana, geneva, sans-serif;\">Por exemplo, Equa\u00e7\u00e3o 14 apresenta a soma das pot\u00eancias de duas hidrel\u00e9tricas quaisquer.<\/span><\/p>\n<figure id=\"attachment_4169\" aria-describedby=\"caption-attachment-4169\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/ex_covar.png\"><img decoding=\"async\" class=\"wp-image-4169\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/ex_covar.png\" alt=\"ex_covar\" width=\"800\" height=\"137\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/ex_covar.png 1423w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/ex_covar-300x51.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/ex_covar-1024x176.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/ex_covar-624x107.png 624w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-4169\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 14. Vari\u00e2ncia da soma das pot\u00eancias de hidrel\u00e9tricas<\/figcaption><\/figure>\n<p style=\"text-align: justify;\" align=\"center\"><span style=\"font-family: verdana, geneva, sans-serif;\">Isto significa que o valor esperado da pot\u00eancia aumenta, mas sua vari\u00e2ncia pode aumentar ou diminuir em fun\u00e7\u00e3o da correla\u00e7\u00e3o entre as vaz\u00f5es. Por isso, o ideal seriam usinas com correla\u00e7\u00f5es negativas para minimizar o risco de faltar energia.<\/span><\/p>\n<h2 id='distor\u00e7\u00e3o-skewness'  id=\"boomdevs_17\"><span style=\"font-family: verdana, geneva, sans-serif;\">Distor\u00e7\u00e3o (Skewness)<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Conforme vimos anteriormente, a m\u00e9dia, moda e mediana nem sempre se igualam. Na verdade, a simetria da distribui\u00e7\u00e3o de probabilidade em rela\u00e7\u00e3o \u00e0 m\u00e9dia consiste em condi\u00e7\u00e3o necess\u00e1ria para que elas sejam iguais.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A <strong>distor\u00e7\u00e3o<\/strong> mede o grau de assimetria da distribui\u00e7\u00e3o de probabilidade de uma vari\u00e1vel aleat\u00f3ria em rela\u00e7\u00e3o ao valor esperado. Define-se a distor\u00e7\u00e3o como sendo o momento ao redor da m\u00e9dia de terceira ordem dividido pelo desvio padr\u00e3o ao cubo.<\/span><\/p>\n<figure id=\"attachment_4352\" aria-describedby=\"caption-attachment-4352\" style=\"width: 227px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/distorcao.png\"><img decoding=\"async\" class=\"wp-image-4352 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/distorcao.png\" alt=\"distorcao\" width=\"227\" height=\"115\" \/><\/a><figcaption id=\"caption-attachment-4352\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 15. Distor\u00e7\u00e3o<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A distor\u00e7\u00e3o pode ser positiva ou negativa conforme a distor\u00e7\u00e3o seja para a direita ou esquerda respectivamente. Distor\u00e7\u00e3o igual a zero significa uma distribui\u00e7\u00e3o perfeitamente sim\u00e9trica em rela\u00e7\u00e3o ao valor esperado, como a distribui\u00e7\u00e3o normal.<\/span><\/p>\n<h2 id='curtose-kurtosis'  id=\"boomdevs_18\"><span style=\"font-family: verdana, geneva, sans-serif;\">Curtose (Kurtosis)<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A curtose mede a probabilidade dos valores extremos da distribui\u00e7\u00e3o de probabilidade ou a probabilidade da moda. Define-se a curtose como o momento de quarta ordem ao redor da m\u00e9dia dividido pelo desvio padr\u00e3o elevado a quatro.<\/span><\/p>\n<figure id=\"attachment_4350\" aria-describedby=\"caption-attachment-4350\" style=\"width: 227px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/curtose.png\"><img decoding=\"async\" class=\"wp-image-4350 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/curtose.png\" alt=\"curtose\" width=\"227\" height=\"115\" \/><\/a><figcaption id=\"caption-attachment-4350\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 16. Curtose<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Utiliza-se a distribui\u00e7\u00e3o de probabilidade normal, que possui curtose de 3 como refer\u00eancia.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Valores menores do que 3 representam distribui\u00e7\u00f5es com extremos reduzidos e valores maiores do que 3 representam distribui\u00e7\u00f5es com extremos mais prov\u00e1veis.<\/span><\/p>\n<h2 id='boxplot'  id=\"boomdevs_19\"><span style=\"font-family: verdana, geneva, sans-serif;\">Boxplot<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Como a estat\u00edstica trabalha com grandes quantidades de dados, surge a necessidade de apresentar informa\u00e7\u00f5es de forma simples e direta. O gr\u00e1fico Boxplot permite apresentar um conjunto importante de grandezas estat\u00edsticas de forma clara e simples.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O ret\u00e2ngulo delimita 50% de probabilidade de ocorr\u00eancia da vari\u00e1vel e se encontra delimitado pelo primeiro quartil <span id='easy-footnote-3-2750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/#easy-footnote-bottom-3-2750' title='25% de probabilidade de ocorr\u00eancia'><sup>3<\/sup><\/a><\/span> e o terceiro quartil <span id='easy-footnote-4-2750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/#easy-footnote-bottom-4-2750' title='75% de probabilidade de ocorr\u00eancia'><sup>4<\/sup><\/a><\/span>. A mediana<span id='easy-footnote-5-2750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/#easy-footnote-bottom-5-2750' title='segundo quartil'><sup>5<\/sup><\/a><\/span>, que representa 50% de probabilidade de ocorr\u00eancia, divide esse ret\u00e2ngulo em duas partes nem sempre iguais.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os valores extremos surgem abaixo do Primeiro Quartil e acima do Terceiro Quartil at\u00e9 valores 1,5 vezes o IQR &#8211; Interquantile Range, que podemos traduzir como Amplitude Interquartil. O valor do fator multiplicativo de 1,5 \u00e9 arbitr\u00e1rio <span id='easy-footnote-6-2750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/#easy-footnote-bottom-6-2750' title=' este \u00e9 o valor padr\u00e3o utilizado no R, mas pode ser ajustado atrav\u00e9s do par\u00e2metro range na fun\u00e7\u00e3o boxplot'><sup>6<\/sup><\/a><\/span>, pode ser ajustado conforme a aplica\u00e7\u00e3o espec\u00edfica.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Propositalmente, a Figura 4 mostra que o fator multiplicativo somente deve ser igual para os pontos superiores e inferiores quando a distribui\u00e7\u00e3o estat\u00edstica dos dados for sim\u00e9trica.<\/span><\/p>\n<figure id=\"attachment_22403\" aria-describedby=\"caption-attachment-22403\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Boxplot1.png\"><img decoding=\"async\" class=\"wp-image-22403 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Boxplot1.png\" alt=\"\" width=\"600\" height=\"800\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Boxplot1.png 600w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Boxplot1-225x300.png 225w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/a><figcaption id=\"caption-attachment-22403\" class=\"wp-caption-text\">Figura 4. Boxplot padr\u00e3o no R<\/figcaption><\/figure>\n<h2 id='lei-dos-grandes-n\u00fameros'  id=\"boomdevs_20\"><span style=\"font-family: verdana, geneva, sans-serif;\">Lei dos Grandes N\u00fameros<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O valor esperado da soma de vari\u00e1veis aleat\u00f3rias mutuamente independentes, cada uma com sua m\u00e9dia e vari\u00e2ncia, tende para a m\u00e9dia aritm\u00e9tica das m\u00e9dias das vari\u00e1veis quando o n\u00famero de vari\u00e1veis tende a infinito. Al\u00e9m disso, a distribui\u00e7\u00e3o de probabilidade da soma de vari\u00e1veis rand\u00f4micas tende para uma distribui\u00e7\u00e3o normal.<\/span><\/p>\n<h2 id='percentis'  id=\"boomdevs_21\"><span style=\"font-family: verdana, geneva, sans-serif;\">Percentis<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A fun\u00e7\u00e3o probabilidade acumulada fornece a probabilidade P para valores menores que X. A fun\u00e7\u00e3o percentil representa a fun\u00e7\u00e3o inversa da fun\u00e7\u00e3o probabilidade acumulada. Dado um valor de probabilidade, ela fornece o valor de X. A figura abaixo mostra a probabilidade acumulada de duas vari\u00e1veis aleat\u00f3rias. Neste caso, o percentil de 50% (mediana) \u00e9 o mesmo para as duas vari\u00e1veis e vale zero. Contudo, os percentis de 25% e 75% s\u00e3o diferentes, eles medem a varia\u00e7\u00e3o da vari\u00e1vel aleat\u00f3ria ao redor da vari\u00e1vel de localiza\u00e7\u00e3o.<\/span><\/p>\n<p style=\"text-align: center;\">\n<div class=\"wdt-wrapper-chart-loader\" data-id=\"129\"\n     style=\"height: 600px;\">\n    <div class=\"wdt-main-item\">\n                <div class=\"wdt-chart-animated-background\" style=\"height: 150px\">\n            <div class=\"wdt-background-masker wdt-btn-divide-left wdt-chart-one\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-2\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-3\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-4 wdt-chart-three\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-5\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-6\"><\/div>\n            <div class=\"wdt-background-masker 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Probabilidade acumulada\u00a0<\/span><\/p>\n<h2 id='s\u00e9ries-temporais'  id=\"boomdevs_22\" align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">S\u00e9ries Temporais<\/span><\/h2>\n<p align=\"justify\"><span lang=\"PT-BR\" style=\"font-family: verdana, geneva, sans-serif;\" xml:lang=\"PT-BR\">Denomina-se de <strong>S\u00e9ries Temporais<\/strong> as fun\u00e7\u00f5es aleat\u00f3rias de uma vari\u00e1vel independente relacionada com o tempo. <\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">A impossibilidade de prever o comportamento futuro caracteriza as s\u00e9ries temporais porque n\u00e3o existe uma fun\u00e7\u00e3o <em>\u2018determin\u00edstica\u2019<\/em> do tempo que represente a s\u00e9rie.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">F\u00f3rmulas matem\u00e1ticas podem prever as \u00f3rbitas de planetas e sat\u00e9lites com precis\u00e3o porque as equa\u00e7\u00f5es da f\u00edsica representam o sistema.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">Por outro lado, fen\u00f4menos naturais, tais como vaz\u00e3o, precipita\u00e7\u00e3o, velocidade do vento, dire\u00e7\u00e3o do vento e irradia\u00e7\u00e3o solar, n\u00e3o podem ser descritos por fun\u00e7\u00f5es matem\u00e1ticas de forma determin\u00edstica.<\/span><\/p>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, podemos descrever estes fen\u00f4menos como um <strong>Processo Estoc\u00e1stico<\/strong>.<\/span><\/p>\n<h3 id='processo-estoc\u00e1stico'  id=\"boomdevs_23\" align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Processo Estoc\u00e1stico<\/span><\/h3>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\">Define-se <strong>Processo Estoc\u00e1stico<\/strong> como uma fam\u00edlia de fun\u00e7\u00f5es aleat\u00f3rias Z(t,w). A vari\u00e1vel t pertence ao conjunto T e a vari\u00e1vel w pertence ao conjunto W. A fun\u00e7\u00e3o Z representa um conjunto de distribui\u00e7\u00f5es de probabilidade que variam com o tempo.<\/span><\/p>\n<p align=\"left\"><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>S\u00e9ries Temporais<\/strong> constituem uma amostragem do conjunto Z(t,w) e podemos interpret\u00e1-las como poss\u00edveis trajet\u00f3rias do processo estoc\u00e1stico no tempo.<\/span><\/p>\n<figure id=\"attachment_22330\" aria-describedby=\"caption-attachment-22330\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/P-estocastico.png\"><img decoding=\"async\" class=\"wp-image-22330 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/P-estocastico.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/P-estocastico.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/P-estocastico-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/P-estocastico-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-22330\" class=\"wp-caption-text\">Figura 6. Processo Estoc\u00e1stico<\/figcaption><\/figure>\n<p align=\"justify\"><span lang=\"PT-BR\" style=\"font-family: verdana, geneva, sans-serif;\" xml:lang=\"PT-BR\">Os <strong>Processos Estoc\u00e1sticos<\/strong> podem ser classificados em:<br \/>\n<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Estacion\u00e1rios;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Normais ou Gaussianos;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Markovianos.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Define-se<strong> Processo Estoc\u00e1stico Estacion\u00e1rio<\/strong> como o processo estoc\u00e1stico que independe da origem dos tempos. Neste caso, as fun\u00e7\u00f5es Z(w) s\u00e3o iguais ao longo do tempo. Isto significa que o processo se encontra em equil\u00edbrio estat\u00edstico. Este conceito \u00e9 matematicamente forte, mas de dif\u00edcil aplica\u00e7\u00e3o.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>Processo Estoc\u00e1stico Estritamente Estacion\u00e1rio<\/strong> representa aquele onde todos os momentos estat\u00edsticos das fun\u00e7\u00f5es Z(w) dependem apenas das diferen\u00e7as t<sub>j<\/sub>-t<sub>i<\/sub>, assim como os momentos de todas as distribui\u00e7\u00f5es bidimensionais [Z<sub>tn<\/sub>, Z<sub>tm<\/sub>]. Este conceito n\u00e3o \u00e9 t\u00e3o forte quanto ao anterior, mas cont\u00ednua de dif\u00edcil aplica\u00e7\u00e3o.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Finalmente,<strong> Processo Estoc\u00e1stico Fracamente Estacion\u00e1rio ou Estacion\u00e1rio de Segunda Ordem<\/strong> \u00e9 aquele onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O valor esperado das fun\u00e7\u00f5es aleat\u00f3rias Z s\u00e3o iguais e constantes ao longo do tempo;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O valor esperado da vari\u00e2ncia de todas as fun\u00e7\u00f5es aleat\u00f3rias Z s\u00e3o finitos;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A covari\u00e2ncia entre todos e quaisquer pares de fun\u00e7\u00f5es aleat\u00f3rias Z<sub>i<\/sub> e Z<sub>j<\/sub> depende apenas do m\u00f3dulo de t<sub>i<\/sub>-t<sub>j<\/sub>.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>Processo Estoc\u00e1stico Gaussiano<\/strong> \u00e9 aquele onde todas as fun\u00e7\u00f5es aleat\u00f3rias Z apresentam distribui\u00e7\u00e3o normal ou gaussiana.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>Processos Estoc\u00e1sticos Markovianos<\/strong> s\u00e3o os processos estoc\u00e1sticos sem mem\u00f3ria.\u00a0 Isto \u00e9, os estados futuros do processo dependem apenas do estado atual do processo.\u00a0<\/span><\/p>\n<h2 id='an\u00e1lise-de-s\u00e9ries-temporais'  id=\"boomdevs_24\"><span style=\"font-family: verdana, geneva, sans-serif;\">An\u00e1lise de S\u00e9ries Temporais<\/span><\/h2>\n<p align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">Existem dois tipos de <strong>modelos de an\u00e1lise de s\u00e9ries temporais<\/strong>; os <strong>param\u00e9tricos<\/strong> e os <strong>n\u00e3o-param\u00e9tricos<\/strong>. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Modelos param\u00e9tricos possuem n\u00famero finitos de par\u00e2metros e os n\u00e3o-param\u00e9tricos possuem infinitos par\u00e2metros.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: verdana, geneva, sans-serif;\">Exemplos de modelos param\u00e9tricos s\u00e3o:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">modelos de erro ou de regress\u00e3o;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">modelos de autorregress\u00e3o e m\u00e9dia m\u00f3vel &#8211; ARMA;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">modelos de autorregress\u00e3o integrada e m\u00e9dias m\u00f3veis &#8211; ARIMA;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">modelos de mem\u00f3ria longa &#8211; ARFIMA;<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Exemplos de modelos n\u00e3o param\u00e9tricos s\u00e3o:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">modelos de autocorrela\u00e7\u00e3o e espectrais; transformada de Fourier e Wavelets.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Toda s\u00e9rie temporal pode ser decomposta numa sequ\u00eancia determin\u00edstica e outra aleat\u00f3ria do tempo.<\/span><\/p>\n<figure id=\"attachment_3183\" aria-describedby=\"caption-attachment-3183\" style=\"width: 292px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/zt_1.png\"><img decoding=\"async\" class=\"wp-image-3183 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/zt_1.png\" alt=\"zt_1\" width=\"292\" height=\"70\" \/><\/a><figcaption id=\"caption-attachment-3183\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 17. Decomposi\u00e7\u00e3o de s\u00e9ries temporais<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Z<sub>t<\/sub> \u00e9 a s\u00e9rie temporal;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">f<sub>t<\/sub> \u00e9 a parte determin\u00edstica ou sinal;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">a<sub>t<\/sub> \u00e9 a parte aleat\u00f3ria ou ru\u00eddo;<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Dependendo do comportamento e caracter\u00edsticas das fun\u00e7\u00f5es <em>f<\/em> e <em>a<\/em>, algumas simplifica\u00e7\u00f5es s\u00e3o poss\u00edveis e os diversos modelos foram desenvolvidos.<\/span><\/p>\n<h3 id='modelos-de-erro-ou-regress\u00e3o'  id=\"boomdevs_25\"><span style=\"font-family: verdana, geneva, sans-serif;\">Modelos de Erro ou Regress\u00e3o<\/span><\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os modelos mais simples, chamados de erro ou regress\u00e3o, ocorrem quando a parte determin\u00edstica da s\u00e9rie temporal independe da parte aleat\u00f3ria e a parte aleat\u00f3ria independe do tempo.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Matematicamente, isto significa que:<\/span><\/p>\n<figure id=\"attachment_3184\" aria-describedby=\"caption-attachment-3184\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_1.png\"><img decoding=\"async\" class=\"wp-image-3184\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_1.png\" alt=\"st_1\" width=\"300\" height=\"252\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_1.png 353w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_1-300x252.png 300w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-3184\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 18. Hip\u00f3teses simplificadores<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>E<\/em> \u00e9 o valor esperado.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Dependendo do tipo de fun\u00e7\u00e3o <em>f<sub>t <\/sub>, <\/em>classifica-se o modelo em:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo de Tend\u00eancia Linear;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo de Regress\u00e3o;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo Oscilat\u00f3rio.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h4 id='modelo-de-tend\u00eancia-linear'  id=\"boomdevs_26\"><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo de Tend\u00eancia Linear<\/span><\/h4>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No modelo de tend\u00eancia linear, a parte determin\u00edstica da s\u00e9rie temporal depende apenas de dois par\u00e2metros constantes; \u03b1 e \u03b2.<\/span><\/p>\n<figure id=\"attachment_3186\" aria-describedby=\"caption-attachment-3186\" style=\"width: 370px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_2.png\"><img decoding=\"async\" class=\"wp-image-3186 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_2.png\" alt=\"st_2\" width=\"370\" height=\"68\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_2.png 370w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_2-300x55.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/a><figcaption id=\"caption-attachment-3186\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 19. Tend\u00eancia linear<\/figcaption><\/figure>\n<h4 id='modelo-de-regress\u00e3o'  id=\"boomdevs_27\"><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo de Regress\u00e3o<\/span><\/h4>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">No modelo de regress\u00e3o, uma fun\u00e7\u00e3o linear de uma vari\u00e1vel observ\u00e1vel dependente do tempo determina a parcela determin\u00edstica da fun\u00e7\u00e3o.<\/span><\/p>\n<figure id=\"attachment_3187\" aria-describedby=\"caption-attachment-3187\" style=\"width: 392px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_3.png\"><img decoding=\"async\" class=\"wp-image-3187 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_3.png\" alt=\"Regress\u00e3o\" width=\"392\" height=\"68\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_3.png 392w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_3-300x52.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/a><figcaption id=\"caption-attachment-3187\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 20. Regress\u00e3o<\/figcaption><\/figure>\n<h4 id='modelo-oscilat\u00f3rio'  id=\"boomdevs_28\">Modelo Oscilat\u00f3rio<\/h4>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Modelos oscilat\u00f3rios utilizam a s\u00e9rie de Fourier, a Transformada de Fourier, a Transformada R\u00e1pida de Fourier e Wavelets. Independentemente da t\u00e9cnica utilizada, o objetivo deste modelo consiste em identificar os modos de oscila\u00e7\u00e3o existentes no processo analisado.\u00a0<\/span><\/p>\n<figure id=\"attachment_3201\" aria-describedby=\"caption-attachment-3201\" style=\"width: 980px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_6.png\"><img decoding=\"async\" class=\"wp-image-3201 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_6.png\" alt=\"S\u00e9rie de Fourier\" width=\"980\" height=\"168\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_6.png 980w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_6-300x51.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_6-624x107.png 624w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/a><figcaption id=\"caption-attachment-3201\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 20. S\u00e9rie de Fourier<\/span><\/figcaption><\/figure>\n<h3 id='modelos-de-auto-regress\u00e3o'  id=\"boomdevs_29\"><span style=\"font-family: verdana, geneva, sans-serif;\">Modelos de Auto-Regress\u00e3o<\/span><\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Admitir a inexist\u00eancia de correla\u00e7\u00e3o entre a vaz\u00e3o<span id='easy-footnote-7-2750' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/geracao-de-energia-eletrica\/series-temporais\/#easy-footnote-bottom-7-2750' title=' vale para todas as grandezas meteorol\u00f3gicas '><sup>7<\/sup><\/a><\/span> de hoje com a vaz\u00e3o de ontem n\u00e3o se sustenta na pr\u00e1tica. O senso comum nos diz que uma boa estimativa do tempo de amanh\u00e3 baseia-se na observa\u00e7\u00e3o do tempo hoje.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, a caracter\u00edstica dos processos estoc\u00e1sticos consiste em variar de forma aleat\u00f3ria essa correla\u00e7\u00e3o.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os modelos de auto-regress\u00e3o permitem representar sistemas f\u00edsicos com correla\u00e7\u00e3o temporal. Existem basicamente tr\u00eas classes de modelos de auto-regress\u00e3o:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Processos Lineares Estacion\u00e1rios;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Processos Lineares n\u00e3o Estacion\u00e1rios Homog\u00eaneos;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Processos de Mem\u00f3ria Longa.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3 id='tend\u00eancia-e-sazonalidade'  id=\"boomdevs_30\"><span style=\"font-family: verdana, geneva, sans-serif;\">Tend\u00eancia e Sazonalidade<\/span><\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Tradicionalmente, os estudiosos decomp\u00f5es as s\u00e9ries temporais em duas parcelas determin\u00edsticas: Tend\u00eancia e Sazonalidade.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_8.png\"><img decoding=\"async\" class=\"aligncenter wp-image-3225 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_8.png\" alt=\"st_8\" width=\"420\" height=\"65\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_8.png 420w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/03\/st_8-300x46.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/a>Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">T<sub>t<\/sub> \u00e9 a tend\u00eancia;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">S<sub>t<\/sub> \u00e9 a sazonalidade;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">a<sub>t<\/sub> \u00e9 a parcela aleat\u00f3ria, que possui m\u00e9dia zero e vari\u00e2ncia \u03c3<sup>2<\/sup><sub>t<\/sub>.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A parcela a<sub>t<\/sub> possui m\u00e9dia zero porque a m\u00e9dia ficou inclu\u00edda na tend\u00eancia.<\/span><\/p>\n<h4 id='tend\u00eancia'  id=\"boomdevs_31\"><span style=\"font-family: verdana, geneva, sans-serif;\">Tend\u00eancia<\/span><\/h4>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A tend\u00eancia pode ser obtida pelos m\u00e9todos de erro ou regress\u00e3o apresentados acima. Em particular, utiliza-se a aproxima\u00e7\u00e3o polinomial. Na pr\u00e1tica, a aplica\u00e7\u00e3o deste m\u00e9todo nos dados brutos pode levar a polin\u00f4mios de ordem muito elevada, que acabam complicando o problema. A maneira elegante de resolver esta quest\u00e3o consiste na aplica\u00e7\u00e3o da aproxima\u00e7\u00e3o polinomial nos dados brutos filtrados.<\/span><\/p>\n<h2 id='refer\u00eancias'  id=\"boomdevs_32\"><span style=\"font-family: verdana, geneva, sans-serif;\">Refer\u00eancias<\/span><\/h2>\n<ol>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">BARTHOLOMEW, D.J., <strong>What is Statistics?,<\/strong>\u00a0J.R. Statist. Soc. A (1995) 158, Part1, pg. 1-20.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">BOX,G.E.P., JENKINS, G.M., REINSEL, G.C., <strong>Time Series Analysis &#8211; Forecasting and Control<\/strong>, 4 edi\u00e7\u00e3o, John Wilwy &amp; Sons, 2008.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">COWPERTWAIT, P.S.P., METCALFE, A.V., <strong>Introductory Time Series with R<\/strong>, Springer, 2009.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">CRYER, J.D., CHN, K.S., <strong>Time Series Analysis with Applications in<\/strong> <strong>R<\/strong>, 2 edi\u00e7\u00e3o, Springer, 2008.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">HSU, H., <strong>Probability, Random Variables &amp; Random Processes<\/strong>, McGraw-Hill, 1997.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">MORETTIN,P.A., TOLOI, C.M.C., <strong>An\u00e1lise de S\u00e9ries Temporais<\/strong>, Edgard Bl\u00fccher, S\u00e3o Paulo, 2004.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">SPIEGEL, M.R., SCHILLER, J., SRINIVASAN, R.A., <strong>Probability and Statistics<\/strong>, 2 edi\u00e7\u00e3o, Cole\u00e7\u00e3o Schaum, McGraw-Hill, 2000.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">WEI, W.S.W., <strong>Time Series Analysis &#8211; Univariate and Multivariate Methods<\/strong>, 2 edi\u00e7\u00e3o, Pearson, 2006.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">WILKS, D. S., <strong>Statistical Methods in the Atmospheric Sciences<\/strong>, 3 edi\u00e7\u00e3o, Elsevier, 2011.<\/span><\/li>\n<\/ol>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-inline: initial; inset: initial; box-shadow: initial; 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paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; max-width: initial; min-block-size: initial; min-height: initial; min-inline-size: initial; min-width: initial; mix-blend-mode: initial; object-fit: initial; object-position: initial; offset: initial; opacity: initial; order: initial; origin-trial-test-property: initial; orphans: initial; outline: initial; outline-offset: initial; overflow-anchor: initial; overflow-wrap: initial; overflow: initial; overscroll-behavior-block: initial; overscroll-behavior-inline: initial; overscroll-behavior: initial; padding-block: initial; padding: initial; padding-inline: initial; page: initial; page-orientation: initial; paint-order: initial; perspective: initial; perspective-origin: initial; pointer-events: initial; position: initial; quotes: initial; r: initial; resize: initial; ruby-position: initial; rx: initial; ry: initial; scroll-behavior: initial; scroll-margin-block: initial; scroll-margin: initial; scroll-margin-inline: initial; scroll-padding-block: initial; scroll-padding: initial; scroll-padding-inline: initial; scroll-snap-align: initial; scroll-snap-stop: initial; scroll-snap-type: initial; shape-image-threshold: initial; shape-margin: initial; shape-outside: initial; shape-rendering: initial; size: initial; speak: initial; stop-color: initial; stop-opacity: initial; stroke: initial; stroke-dasharray: initial; stroke-dashoffset: initial; stroke-linecap: initial; stroke-linejoin: initial; stroke-miterlimit: initial; stroke-opacity: initial; stroke-width: initial; tab-size: initial; table-layout: initial; text-align: initial; text-align-last: initial; text-anchor: initial; text-combine-upright: initial; text-decoration: initial; text-decoration-skip-ink: initial; text-indent: initial; text-overflow: initial; text-shadow: initial; text-size-adjust: initial; text-transform: initial; text-underline-offset: initial; text-underline-position: initial; touch-action: initial; transform: initial; transform-box: initial; transform-origin: initial; transform-style: initial; transition: initial; user-select: initial; vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; clip-path: initial; clip-rule: initial; color-interpolation: initial; color-interpolation-filters: initial; color-rendering: initial; color-scheme: initial; columns: initial; column-fill: initial; gap: initial; column-rule: initial; column-span: initial; contain: initial; contain-intrinsic-size: initial; content: initial; content-visibility: initial; counter-increment: initial; counter-reset: initial; counter-set: initial; cursor: initial; cx: initial; cy: initial; d: initial; display: block; dominant-baseline: initial; empty-cells: initial; fill: initial; fill-opacity: initial; fill-rule: initial; filter: initial; flex: initial; flex-flow: initial; float: initial; flood-color: initial; flood-opacity: initial; grid: initial; grid-area: initial; height: 0px; hyphens: initial; image-orientation: initial; image-rendering: initial; inline-size: initial; inset-block: initial; inset-inline: initial; isolation: initial; letter-spacing: initial; lighting-color: initial; line-break: initial; list-style: initial; margin-block: initial; margin: initial; margin-inline: initial; marker: initial; mask: initial; mask-type: initial; max-block-size: initial; max-height: initial; max-inline-size: initial; 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