 On the product of two harmonizable time seriesDominique Dehay Stochastic Processes and their Applications, 1991, vol. 38, issue 2, 347-358 Abstract: In order to state sufficient conditions for the harmonizability of the product time series of two harmonizable time series, the notion of Lp-harmonizable time series is introduced for 1 [less-than-or-equals, slant] p [less-than-or-equals, slant] + [infinity]. Then, the problem of the product of two stochastic measures is tackled and Fubini type theorems are deduced. We derive sufficient conditions for the harmonizability of a weighted convolution time series of two harmonizable time series. As an application to nonlinear prediction theory, asymptotically unbiased estimors for values of the cross spectral bimeasure of two harmonizable time series are given. The L1-convergence of these estimators towards some random variables is established from the law of large numbers stated for Lp-harmonizable series. Sufficient conditions for the a.e. convergence are obtained from the strong law of large numbers. The case of two jointly stationary harmonizable series is also considered. The results apply to the estimation of the asymptotic spectral measure of some asymptotically stationary series. Date: 1991 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:38:y:1991:i:2:p:347-358 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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