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Moving Averages of Random Vectors with Regularly Varying Tails
Author(s) -
Meerschaert Mark M.,
Scheffler HansPeter
Publication year - 2000
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00187
Subject(s) - mathematics , autocovariance , operator (biology) , limit (mathematics) , domain (mathematical analysis) , central limit theorem , law of large numbers , distribution (mathematics) , mathematical analysis , random variable , statistics , biochemistry , chemistry , repressor , fourier transform , transcription factor , gene
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.