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Invariance principles for tempered fractionally integrated processes

Farzad Sabzikar and Donatas Surgailis

Stochastic Processes and their Applications, 2018, vol. 128, issue 10, 3419-3438

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 limN→∞λ∕N=λ∗. 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<λ∗<∞) cases. These results are used to derive the limit distribution of the ordinary least squares estimate of AR(1) unit root with weakly, strongly, and moderately tempered moving average errors.

Keywords: Invariance principle; Tempered linear process; Autoregressive fractionally integrated moving average; Tempered fractional stable/Brownian motion; Tempered fractional unit root distribution (search for similar items in EconPapers)
Date: 2018
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