Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8954745 | Stochastic Processes and their Applications | 2018 | 20 Pages |
Abstract
We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in α-stable (1<αâ¤2) i.i.d. innovations and related tempered linear processes with vanishing tempering parameter limNââλâN=λâ. We show that the limit of the partial sums process takes a different form in the weakly tempered (λâ=0), strongly tempered (λâ=â), and moderately tempered (0<λâ<â) 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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Farzad Sabzikar, Donatas Surgailis,