On the asymptotic independence of the sum and rare values of weakly dependent stationary random variables

It is shown that if the stationary sequence {Xi} has finite variance and satisfies a certain mixing condition, then the asymptotic distribution of [summation operator]ni=1 Xn is unaffected by the information of whether the summands are in certain "rare" sets. An application of the result shows that [summation operator]ni=1 Xi and the extremes of X1,...,Xn are asymptotically independent. This is in sharp contrast to the infinite variance case.

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Year of publication:	1995
Authors:	Hsing, Tailen
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 60.1995, 1, p. 49-63
Publisher:	Elsevier
Keywords:	Central limit theorem Extreme value Mixing condition Point process

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008875656