By Planas A.

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Extra info for Applied Time Series Analysis.Modelling,Forecasting,Unobserved Components Analysis & the Wiener-Kolmogorov Filter.(172p)

Example text

The Acf shows signi cant correlations at lags 1 and 12. The partial correlations at lags 1 and 12 are also signi cant, but they are followed by signi cant autocorrelations at lags 2 and 13, 14. This information leads to consider the airline model (0 1 1)(0 1 1)12 as a possible candidate for describing the autocorrelation structure of this series. Example 3: Series Itpdb428 The series Itpdb428 represents the monthly italian production of soft drinks. It extends from january 1985 to november 1993, that is along a sample of 107 observations.

Models for the seasonal part of time series most often belong to the class of the (1; 1; 1)s , (0; 1; 1)s , (1; 0; 1)s or (1; 1; 0)s models. 5 ........................................................................................................................................................................................................................................................................................................................................................................

Although some tests have been constructed for that (see Dickey and Fuller (1979), Phillips (1987)), the Acf may also be used. Consider the random walk for which we had yt = y0 + et + et01 + 1 1 1 + e1. It is readily seen that cov(yt; yt0k ) = (t 0 k)V (et). Thus the theoretical autocorrelations will be (k) = (t 0 k)=t: the autocorrelations fall o slowly as k increases. In practice, the sample autocorrelations tend to follow the behavior of the theoretical autocorrelations, and so failure of the autocorrelations to die out quickly is a strong indication of nonstationarity.

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Applied Time Series Analysis.Modelling,Forecasting,Unobserved Components Analysis & the Wiener-Kolmogorov Filter.(172p) by Planas A.


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