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

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, α∈(0,2), α = 2, and α∈(2,∞). The limiting distribution of the Dickey-Fuller (DF) unit-root test is shown to be a functional of two stable processes when α∈(0,2) and a functional of a standard Brownian motion when α∈[2,∞). Since the limit distribution contains some nuisance parameters, it is difficult, if not impossible, to be estimated. This is especially the case when α∈(1,2). 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.