Moving Averages of Random Vectors with Regularly Varying Tails

Mark M. Meerschaert and Hans‐Peter Scheffler

Journal of Time Series Analysis, 2000, vol. 21, issue 3, 297-328

Abstract: Regular variation is an analytic condition on the tails of a probability distribution which is necessary for an extended central limit theorem to hold, when the tails are too heavy to allow attraction to a normal limit. The limiting distributions which can occur are called operator stable. In this paper we show that moving averages of random vectors with regularly varying tails are in the generalized domain of attraction of an operator stable law. We also prove that the sample autocovariance matrix of these moving averages is in the generalized domain of attraction of an operator stable law on the vector space of symmetric matrices. AMS 1990 subject classification. Primary 62M10, secondary 62E20, 62F12, 60F05.

Date: 2000
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