A Darling–Erdös type result for stationary ellipsoids

Let {Xk,k∈Z} be a zero mean d-dimensional stationary process, and let Sn,d=(Sn,1,Sn,2,…,Sn,d)T with Sn,h=1n∑k=1nXk,h, where Xk,h denotes the single components of {Xk,k∈Z}. Under a weak dependence condition, we show that the ellipsoid Xd2=max1≤k≤d(2k)−1/2|Sn,kTΓk−1Sn,k−k| follows a Darling–Erdös type law as d→∞, i.e., Xd2 converges to a Gumbel-type distribution exp(−e−z). We show that this result is valid as long as d→∞ and d=dn=O(nd) with d>0.

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Year of publication:	2013
Authors:	Jirak, Moritz
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 123.2013, 6, p. 1922-1946
Publisher:	Elsevier
Subject:	Asymptotic extreme value distribution \| Weakly dependent processes

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

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