Periodic moving averages of random variables with regularly varying tails. (English) Zbl 0900.62488

Anderson, Paul L.; Meerschaert, Mark M.

Ann. Stat. 25, No. 2, 771-785 (1997).

Summary: 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 seasons. 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.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20	Asymptotic distribution theory in statistics
60F05	Central limit and other weak theorems

Keywords:

moving averages; autocorrelation; autocovariance; regular variation; domains of attraction

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