sÃ©ries univariantes de tempo - metodologia de Box & Jenkins

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ABSTRACTThe present dissertation is concerned with the method developed byGeorge E. P. Box and Gwilym M. Jenkins.That methodology was developed during the sixties and published by theauthors in 1970 under the title "Time series analysis: forecasting andcontrol".The significance of Box and Jenkins' work is given by the possibilityof constructing linear models of the autoregressive integrated movingaverage type that could describe with precision and parsimony the stochasticprocess that generates a time series, offering therefore accurateforecasts.The strategy in that methodology consists in identifying models ableto describe the data available, to efficiently estimate its parametersand to evaluate the model "vis-S-vis" the phenomenon being invéstigated.If this representation of the real world is adequate, the model can beapplied in time series analysis or, on the contrary, if that representationis not adequate, a new model should be designed and a new roundof tests run.The present dissertation is structured in seven chapters.Chapter I consists of not only the general question being posed andour concern about it justified, but we also develop the fundamentalideas to deal with time series analysis: a short history of the subject,the importance and the statiscal meaning of the technique and the conceptproper of time series.In the chapter II we develop the basic concepts of Stochastic Processthat will be useful for the understanding and working of Box andJenkins' methodology.In chapters III, IV and V we deal in detail with Box and Jenkins 1 timeseries analysis: the models they use, the process of modeling and themethod for forecasting.In chapter VI, we apply the proceding developments to two sets of data,which are significant to the understanding of Rio Grande do Sul economy:the Consumer Price Index (cost of living index) in the city of PortoAlegre and Electric Energy Comsumption in the State. 11 can be observedthat the forecasts obtained through Box and Jenkins' method showvalues very much close to the real data, making it clear about theusefulness of the author's methodology.The last chapter is a summary of the method discussed. We call attentionto its qualities but also to its operational shortcomings and we referto some other methods for time series analysis, trying to locate aspectsfor applying each one of them.
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(/Jmt/)pllllllFundação de Economi
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SUMÁRIOLISTA DE FIGURAS 5LISTA DE
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LISTA DE FIGURASCAPÍTULO 2Figura l
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Figura 22 — Gráfico da PAC da s
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Quadro 13 - Relatório de saída do
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A presente dissertação, orientada
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14de Cournot e Walras, entre outros
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16que as atividades de pesquisa alc
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18funcionamento da realidade econô
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20quatro componentes e tem-se como
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2 - SOBRE SÉRIES TEMPORAISE PROCES
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25onde o segundo membro dessa equa
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A importância do conhecimento de a
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O tipo de não estacionariedade mos
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Essa padronização e obtida atrav
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=t1 p1 ' t-1( 1 o1 ' ' t-2-fl-He 1
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35l M l l l l l lFigura 3 - Correlo
Page 36 and 37:
Para retirar a sazonalidade, cria-s
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40Nesse caso,E (X t ) = E(u+ E(a t
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42Portanto.tSZ = ",z = . E z. = .E.
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44Note-se que, para esse processo,
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463.2 — Modelo Média MóvelSeja
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48Processo Média Móvel de Primeir
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50Y2 = E(a t - 6 1 a t _ 1 '^t^ (a
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Conforme se viu no iteia 3,1, para
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54Coeficiente de autocorrelação>k
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56se k = 2, p 2 = "í^p-, + ií ) 2
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58Portanto,5 = 'i' 1 (B) 8 (B)2 ql
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60Para k < q, o processo misto auto
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62Coeficientes de autocorrelação^
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64Observe-se que, se d=0, o modelo
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66Portanto, o modelo descrito pela
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4 - O PROCESSO DE MODELAGEMOs model
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71/Ml-UIAFigura 1 - Gráfico "Ampli
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O processo de transformação da se
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autocorrelaçao de um processo méd
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'kkhi,.1 O O 1 2l0 2 4 j 618l l 10
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79l 2 3 4 5l M'-''> OO 11 3 l 5 l 7
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81Padrões de p ^ e (4 ^ para um AR
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Na prática, porém, surge outro pr
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Por fim, o estudo das funções de
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Esses vetores serão $,6, e a , de
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Um exemplo pratico permite maior cl
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Para o calculo de S(_$,ô_), os [ a
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para iniciar o processo que se arbi
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95Porque os [e.t/S,wn não são exa
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Esse processo de checagem, em geral
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aparecem escassamente no correlogra
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5-0 MÉTODO DE PREVISÃODE BOX & JE
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103De maneira semelhante, pode-se o
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105Previsão utilizando equação d
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107ou seja,para h > 2,x t (h) = ^^(
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109O valor de x no período t+h éx
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1 11para h=2 ,x t (2) = E, para h >
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Se as previsões para um, dois e tr
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115Portanto o valor de x no tempo t
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6.1 - Nota Introdutória6 - APLICA
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119rie se caracteriza por apresenta
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tricamente crescente, pode-se infer
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123Figura 5 - Gráfico da função
Page 122 and 123: 125Quadro 2Figura 7 — Gráfico da
Page 124 and 125: 127Quadro 4Figura 8 - Gráfico da f
Page 126 and 127: 129Portanto o modelo suposto inicia
Page 128 and 129: 1 JF jR.LN i"ÍSSSÉÍ"'*?!!['"Ortu
Page 130 and 131: 133O Quadro 5 permite algumas consi
Page 132 and 133: 135T»E-EST!«»Tto «E51FWALS-- MO
Page 134 and 135: 137Quadro 6Relatório de saída do
Page 136 and 137: 1396.3 - Previsões para o Consumo
Page 138 and 139: 141A avaliação da necessidade de
Page 140 and 141: 143A Figura 16 permite observar que
Page 142 and 143: 145A ACF da serie V 2 T t (Figura 1
Page 144 and 145: '147Quadro 9Valores numéricos da A
Page 146 and 147: 149Quadro 11Valores numéricos da P
Page 148 and 149: Quadro 12151Principais informaçõe
Page 150 and 151: 1536.3.4 — PrevisõesPara essa se
Page 152 and 153: 155xx* *XXKx**xx*xx*xxxx /x ^x *xAA
Page 154 and 155: 157Figura 24 — Relatório de saí
Page 156 and 157: 160cionarem previsões bastante sat
Page 158 and 159: 162- KIRBY (1966), comparando os m
Page 160 and 161: ANEXO lManual dos Comandos Necessá
Page 162 and 163: 168cc 9-16 Number with four decimai
Page 164 and 165: 170Repeat in cc 17-24, 25-32, etc.
Page 166 and 167: 17240.12345cc 1-5Enter a zero if wi
Page 168 and 169: ANEXO 11Relatórios de Saída do Co
Page 170 and 171: s^c; c —)c i- >C-' "*> — < Sj=
Page 174 and 175: BIBLIOGRAFIAAKAIKE, H. A new look a
Page 176 and 177: MAKRIDAKIS, S. & WHEELWRIGHT, S. C.
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