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Moving Averages of Random Vectors with Regularly Varying Tails
Article first published online: 4 JAN 2002
DOI: 10.1111/1467-9892.00187
Blackwell Publishers Ltd 2000
1467-9892/asset/cover.gif?v=1&s=eec782011cf3959dc4aa59555e8f84f3d4459106 "Journal of Time Series Analysis")
Additional Information
How to Cite
Meerschaert, M. M. and Scheffler, H.-P. (2000), Moving Averages of Random Vectors with Regularly Varying Tails. Journal of Time Series Analysis, 21: 297–328. doi: 10.1111/1467-9892.00187
Publication History
- Issue published online: 4 JAN 2002
- Article first published online: 4 JAN 2002
- Abstract
- Cited By
Keywords:
- Moving average;
- autocovariance matrix;
- operator stable;
- regular variation;
- random matrix
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.