Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 124, Issue 10, Pages 3441-3462Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spa.2014.05.001
Keywords
Trimming; Heavy tails; Asymptotic normality; Autoregressive(1) processes; CUSUM processes
Categories
Funding
- Austrian Science Fund [P24302-N18, W1230]
- Hungarian Scientific Research Fund [K 108615]
- National Science Foundation [DMS 1305858]
- Austrian Science Fund (FWF) [P 24302] Funding Source: researchfish
- Austrian Science Fund (FWF) [P24302] Funding Source: Austrian Science Fund (FWF)
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1305858] Funding Source: National Science Foundation
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In this paper we investigate the distribution of trimmed sums of dependent observations with heavy tails. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. We show if the d largest (in magnitude) terms are removed from the sample, then the sum of the remaining elements satisfies a functional central limit theorem with random centering provided d = d(n) >= n(gamma) (for some gamma > 0) and d(n)/n -> 0. This result is used to get asymptotics for the widely used CUSUM process in case of dependent heavy tailed observations. (C) 2014 Elsevier B.V. All rights reserved.
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