Applied Time Series by Planas A.

By Planas A.

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

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The slow decay of the sample autocorrelations is very apparent. The series needs thus di erencing to become stationary. In the same time, the Pacf shows a very large rst-lag partial autocorrelation, suggesting one single di erence should be enough to obtain stationarity. 2 shows now the sample Acf and Pacf of 1zt, together with their con dence interval. Di erencing zt has completely modi ed the aspect of the sample Acf, which is now much more stable. 5 -1 con dence interval. Depending on the pattern displayed the successive autocorrelations, this is an indication of either an Ar process or of a MA process.

16, together with their respective con dence interval. For the Poem2640 residuals, a reduction in the variance may be seen in the second half of the sample. For the two other series, no particular pattern can be seen: the residuals seem to be white noises. A deeper evaluation of the randomness hypothesis requires to compute the statistics previously described. 04 ........................................................................................................................................................................................................................

This is an evidence of = 1, which is further con rmed by the Pacf which shows a close-to-one peak at lag 12. 4 that the Acf of 112 shows a slow convergence, while the Pacf display a large rst partial autocorrelation. This suggests to consider = 1. 4 shows the Acf and Pacf of 1112 : no need for further di erencing appear. 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.

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