Invariance Principles for Tempered Fractionally Integrated Processes

2017/03/07 by Sabzikar, Farzad, Surgailis, Donatas · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1703.02467

Abstract

We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in α-stable (1< α≤ 2) i.i.d. innovations and related tempered linear processes with vanishing tempering parameter λ∼ λ_*/N. We show that the limit of the partial sums process takes a different form in the weakly tempered (λ_* = 0), strongly tempered (λ_* = ∞), and moderately tempered (0

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