On the validity of the residual-based bootstrap for the unit root test statistic with long memory observations. Issue 2 (1st February 2023) - Fu, Ke-Ang; Li, Jie
Abstract: Consider the AR(1) model, X t = θ X t − 1 + u t, where { u t ; t ≥ 1 } is a sequence of long memory processes with possibly infinite variance. In this paper, we propose to use a residual-based m -out-of- n bootstrap procedure to approximate the distribution of a least-squares estimator for the autoregressive parameter when this parameter is equal to unity, and its asymptotic validity is also proved.