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