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Moving Averages of Random Vectors with Regularly Varying Tails

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  • Mark M. Meerschaert
  • Hans‐Peter Scheffler

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.

Suggested Citation

  • Mark M. Meerschaert & Hans‐Peter Scheffler, 2000. "Moving Averages of Random Vectors with Regularly Varying Tails," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(3), pages 297-328, May.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:3:p:297-328
    DOI: 10.1111/1467-9892.00187
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    Cited by:

    1. Owada, Takashi, 2019. "Topological crackle of heavy-tailed moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4965-4997.
    2. Fasen, Vicky, 2013. "Statistical estimation of multivariate Ornstein–Uhlenbeck processes and applications to co-integration," Journal of Econometrics, Elsevier, vol. 172(2), pages 325-337.

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