Applied Time Series Analysis I. Proceedings of the First by D.F. Findley
By D.F. Findley
Read Online or Download Applied Time Series Analysis I. Proceedings of the First Applied Time Series Symposium Held in Tulsa, Oklahoma, May 14–15, 1976 PDF
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Extra resources for Applied Time Series Analysis I. Proceedings of the First Applied Time Series Symposium Held in Tulsa, Oklahoma, May 14–15, 1976
5) are invertible, then the series generated may have interesting properties. For example, suppose x t is formed by where E t is a Gaussian zero-mean white noise, then and all T '1 0, so that x t will appear to be white noise if just covariances are considered even though it is potentially forecastable from its own past, although in a non-linear fashion. However, it may be shown that this model is never invertible, for any non-zero value of a, and so in practice it cannot be used for forecasting.
Gray et al. 54 THEOREM 7. ) Hn(m+ ) [l;f;+J')' l -- n J ' n+l J ' (m+l) (m) Hn +l [l;f i + j ) and Hn + 2 [1;f i + j ) ~ not ~, then 4 G(m) n+l G (m+l) _ G (m) n n G (m) + n (29) 1 - R (m) n+l where (m+1) r n+l r(m) n+l R(m) n+l (30) In order to calculate the G-transform recursively, it is clear from (29) that a recursive calculation of R~~i also is needed. This is accomplished by the following relations which also were established in [51). [Sns r (m+l) n (m) r n +1 lmHl n (m) -1] , -r n (m+l) s.
Use the algo~ithm o~ Pye and A~chison described above to calculate the G (J), si (J), and r (J) recursively to some i i preassigned maximum values of i and j. Select the proper G. (j) as G-spectral estimator from the "stabling off" p~operty. If Gi (j) does not stable off, inspect the r. (j) and si (j) to determine p and q. 5, and near peaks), it is recommended that the r. J and J. si (j) be considered for possibly a better choice of j and i 60 H. L. Gray et al. in G (j). This procedure is implemented in the program i given in Appendix 2.