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April 1997 Periodic moving averages of random variables with regularly varying tails
Paul L. Anderson, Mark M. Meerschaert
Ann. Statist. 25(2): 771-785 (April 1997). DOI: 10.1214/aos/1031833673


In this paper we establish the basic asymptotic theory for periodic moving averages of i.i.d. random variables with regularly varying tails. The moving average coefficients are allowed to vary according to the season. A simple reformulation yields the corresponding results for moving averages of random vectors. Our main result is that when the underlying random variables have finite variance but infinite fourth moment, the sample autocorrelations are asymptotically stable. It is well known in this case that sample autocorrelations in the classical stationary moving average model are asymptotically normal.


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Paul L. Anderson. Mark M. Meerschaert. "Periodic moving averages of random variables with regularly varying tails." Ann. Statist. 25 (2) 771 - 785, April 1997.


Published: April 1997
First available in Project Euclid: 12 September 2002

zbMATH: 0900.62488
MathSciNet: MR1439323
Digital Object Identifier: 10.1214/aos/1031833673

Primary: 62M10
Secondary: 60F05 , 62E20

Keywords: Autocorrelation , autocovariance , domains of attraction , moving average , regular variation

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 2 • April 1997
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