Journal of Applied Probability

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

Sidney I. Resnick and Joyjit Roy

Abstract

We look at joint regular variation properties of MA(∞) processes of the form X = (Xk, kZ), where Xk = ∑j=0ψjZk-j and the sequence of random variables (Zi, iZ) 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.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 267-279.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528480

Digital Object Identifier
doi:10.1239/jap/1417528480

Mathematical Reviews number (MathSciNet)
MR3317363

Zentralblatt MATH identifier
1334.60049

Subjects
Primary: 28A33: Spaces of measures, convergence of measures [See also 46E27, 60Bxx] 60G70: Extreme value theory; extremal processes
Secondary: 37M10: Time series analysis

Keywords
Regular variation multivariate heavy tail hidden regular variation moving average process

Citation

Resnick, Sidney I.; Roy, Joyjit. Hidden regular variation of moving average processes with heavy-tailed innovations. J. Appl. Probab. 51A (2014), 267--279. doi:10.1239/jap/1417528480. https://projecteuclid.org/euclid.jap/1417528480


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