Bootstrap unit root inference for linear processes of possibly heavy-tailed GARCH-type noises

Abstract.: Over the last 20 years, there has been an interest in unit root inference in the presence of infinite-variance noises. This article studies the unit root with errors being a short-memory linear process of the heavy-tailed GARCH noises with its tail-index, (Formula presented.), α = 2, and (Formula presented.). The limiting distribution of the Dickey-Fuller (DF) unit-root test is shown to be a functional of two stable processes when (Formula presented.) and a functional of a standard Brownian motion when (Formula presented.). Since the limit distribution contains some nuisance parameters, it is difficult, if not impossible, to be estimated. This is especially the case when (Formula presented.). To solve this problem, we propose an m-out-of-n centered residual-based block bootstrap (RBB), which is shown to have the same limit distribution as that of DF test and can be applied to both finite-variance and infinite-variance cases. Simulation studies and a real data analysis show that this RBB approach works well.