Mixed-Norm Spaces and Prediction of S[alpha]S Moving Averages

Suppose that Z k k =-[infin] [infin] is an i.i.d. symmetric [alpha]-stable noise, 1 < [alpha] < 2, and consider the moving average process X k k =-[infin] [infin] given by X k =∑ j =0 [infin] a j Z k -j. Conditions are obtained for the convergence rate of the moving average series, as well as...

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Bibliographic Details
Published inJournal of time series analysis Vol. 36; no. 6; p. 853
Main Authors Cheng, Raymond, Harris, Charles B
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.11.2015
Subjects
Mathematics
Statistics
Studies
Time series
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Summary:Suppose that Z k k =-[infin] [infin] is an i.i.d. symmetric [alpha]-stable noise, 1 < [alpha] < 2, and consider the moving average process X k k =-[infin] [infin] given by X k =∑ j =0 [infin] a j Z k -j. Conditions are obtained for the convergence rate of the moving average series, as well as that of the inverted (autoregressive) representation Z k =∑ j =0 [infin] c j X k -j. These conditions are expressed in terms of the associated function F (z )=∑ j =0 [infin] a j z j and its reciprocal belonging to certain mixed-norm spaces of functions on the open unit disc. Properties of these spaces are explored. Criteria are also derived for the rate of mixing in a certain sense.
ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12134