1. Iowa State University, United States;2. Vilnius University, Lithuania
Abstract:
We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in -stable i.i.d. innovations and related tempered linear processes with vanishing tempering parameter . We show that the limit of the partial sums process takes a different form in the weakly tempered (), strongly tempered (), and moderately tempered () 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.