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# Secular Series

2. Methodology Statistics 2.1. Data The data used in this work are referring to the costs in Reals (R\$) of the commercialized basic basket, in the city of Belm of Par of January of 2005 the December of 2009. is referenciados by the Intersyndical Department of Statisticians and Socioeconmicos Studies (DIEESE). 2.2. Analysis of Secular Series A secular series is a particular accomplishment of a random process of a variate that evolves and keeps a structure of dependence in the time, where the objective is shape this dependence and to transform the series into a white noise. Shape the basic tool a secular series is the autocorrelao function.

The autocorrelao of a process (series) is a standardized measure of the linear dependence of lag K, defined for: (theoretician). The serial dependence is denoted when: for all lags 1, 2, 3, autocorrelao esteem of lag K is defined by: Whose graph is called correlograma and can be used to identify characteristic of a secular series. The shape objective of a secular series, consists of becoming the random process purely called white noise. A white noise is a null sequncia of comments with constant average and variance and autocorrelaes in all lags. In the practical one, if a secular series shows a dependence structure, must be found optimum mathematical model that describes this serial dependence it transforms and it into a white noise. For such, the methodology of Box and Jenkins can be used.

2.2.1. Methodology of Box and Jenkins According to Morettin and Toloi (2004), a methodology sufficiently used in the analysis of parametric models is known as boarding of Box and Jenkins. The methodology consists of adjusting integrated auto-regressive models of mobile averages, ARIMA (p, d, q), to a data set. The strategy for construction of the representative adequate model of the secular series is based on an iterative cycle, on which the choice of the structure of the model is based on the proper data.