Limit theory for random coefficient autoregressive process under possibly infinite variance error sequence. Issue 12 (17th June 2016)

• Record Type: Journal Article
• Authors: Zhou, Zhiyong; Lin, Zhengyan
• Is Part Of: Communications in statistics. Volume 45:Issue 12(2016)
• Page Start: 3562
• Page End: 3576
• Publication Date: 2016-06-17
• Subjects: Asymptotic normality -- Possibly infinite variance -- Random coefficient autoregressive.; 60F05, 62F12; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.904354
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: An asymptotic theory was given by Zhang and Yang (2010 ) for first-order random coefficient autoregressive time series yt = (ρ n + φ n ) y t − 1 + ut, t = 1, …, n, with { ut } is a sequence of independent and identically distributed random variables with mean 0 and a finite second moment, ρ n is a sequence of real numbers, and φ n is a sequence of random variables. Conditional least squares estimator was shown to be asymptotically normality distributed. This model extended the moderate deviations from a unit root model proposed by Phillips and Magdalinos (2007 ), which just considered the case that ρ n = 1 + c / kn and φ n ≡ 0. In this paper, we show that the asymptotic theory in Zhang and Yang (2010 ) still holds when the truncated second moment of the errors l ( x ) = E [ u 2 1 1{| u 1 | ⩽ x }] is slowly varying function at ∞. Moreover, we propose a pivot for, the limit distribution of which is proved to be standard normal.