Asymptotic properties of the bootstrap unit root test statistic under possibly infinite variance. Issue 11 (2nd June 2016)

• Record Type: Journal Article
• Authors: Fu, Ke-Ang; Li, Jie; Yang, Xiao-Rong
• Is Part Of: Communications in statistics. Volume 45:Issue 11(2016)
• Page Start: 3158
• Page End: 3167
• Publication Date: 2016-06-02
• Subjects: Asymptotic distribution -- bootstrap -- domain of the normal law -- unit root test.; 60F05 -- 62F40 -- 62M10; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.901362
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this article, the unit root test for the AR(1) model is discussed, under the condition that the innovations of the model are in the domain of attraction of the normal law with possibly infinite variances. By using residual bootstrap with sample size m < n ( n being the size of the original sample), we bootstrap the least-squares estimator of the autoregressive parameter. Under some mild assumptions, we prove that the null distribution of the unit root test statistic based on the least-square estimator of the autoregressive parameter can be approximated by using residual bootstrap.