Limit theory for random coefficient autoregressive process under possibly infinite variance error sequence

作者：Zhou, Zhiyong^*; Lin, Zhengyan

来源：Communications in Statistics - Theory and Methods, 2016, 45(12): 3562-3576.

DOI：10.1080/03610926.2014.904354

• Asymptotic normality
• Possibly infinite variance
• Random coefficient autoregressive
• 60F05
• 62F12

An asymptotic theory was given by Zhang and Yang (2010) for first-order random coefficient autoregressive time series y(t) = ((n) + phi(n))y(t - 1) + u(t), t = 1, ..., n, with {u(t)} is a sequence of independent and identically distributed random variables with mean 0 and a finite second moment, (n) is a sequence of real numbers, and phi(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 (n) = 1 + c/k(n) and phi(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(1)(2)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.

• 出版日期2016
• 单位浙江大学