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

2013/09/30 by Resnick, Sideny I., Roy, Joyjit · 1 citation
#28A33 #37M10 #60G70 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1309.7909

Abstract

We look at joint regular variation properties of MA(∞) processes of the form X = (X_k, k ∈ ℤ) where X_k = ∑_j=0^∞ ψ_j Z_k-j and the sequence of random variables (Z_i, i ∈ ℤ) are i.i.d. with regularly varying tails. We use the setup of \mathbbM_\mathbbO-convergence and obtain hidden regular variation properties for X under suitable summability conditions on the constant coefficients (ψ_j : j ≥ 0). Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.

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