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Hidden regular variation of moving average processes with heavy-tailed innovations

Part of: Classical measure theory Approximation methods and numerical treatment of dynamical systems Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Sidney I. Resnick  and
Joyjit Roy
Sidney I. Resnick
Affiliation:
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: sir1@cornell.edu.
Joyjit Roy
Affiliation:
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: jr653@cornell.edu.
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Abstract

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We look at joint regular variation properties of MA(∞) processes of the form X = (Xk, k ∈ Z), where Xk = ∑j=0∞ψjZk-j and the sequence of random variables (Zi, i ∈ Z) are independent and identically distributed with regularly varying tails. We use the setup of MO-convergence and obtain hidden regular variation properties for X under summability conditions on the constant coefficients (ψj: j ≥ 0). Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.

Keywords

Regular variationmultivariate heavy tailhidden regular variationmoving average process

MSC classification

Primary: 28A33: Spaces of measures, convergence of measures 60G70: Extreme value theory; extremal processes
Secondary: 37M10: Time series analysis
Type
Part 6. Heavy tails
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 267 - 279
Copyright
Copyright © Applied Probability Trust 2014 

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