Periodic moving averages of random variables with regularly varying tails, Ann

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 au-tocorrelations are asymptotically stable. It is well known in this case that sample autocorrelations in the classical stationary moving average model are asymptotically normal. Introduction. Regular variation is used to characterize those i.i.d. se-quences of random variables for which a version of the central limit theorem holds. When these random variables have infinite variance, the sum is asymp-totically stable instead of asymptotically normal. Stable random variables have found many practical applications beginning with the work of Holts