On the validity of the residual-based bootstrap for the unit root test statistic with long memory observations. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: Fu, Ke-Ang; Li, Jie
• Is Part Of: Communications in statistics. Volume 52:Issue 2(2023)
• Page Start: 309
• Page End: 319
• Publication Date: 2023-02-01
• Subjects: Asymptotic distribution -- bootstrap estimator -- long memory -- unit root; 62F40 -- 60F05; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2020.1855446
• Languages: English
• ISSNs: 0361-0918

Abstract

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.