A Darling–Erdös type result for stationary ellipsoids

Moritz Jirak

Stochastic Processes and their Applications, 2013, vol. 123, issue 6, 1922-1946

Abstract: 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.

Keywords: Asymptotic extreme value distribution; Weakly dependent processes (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414913000379
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:6:p:1922-1946

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2013.01.018

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().