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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… Click to show full abstract
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 lim N → ∞ 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.
Journal Title: Stochastic Processes and their Applications
Year Published: 2017
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