Asymptotic inference for a nonstationary double AR(1) model

Abstract

We investigate the nonstationary double ar(1) model, where ω > 0, α > 0, the η t are independent standard normal random variables and E log |ϕ + η t √α| ⩾ 0. We show that the maximum likelihood estimator of (ϕ, α) is consistent and asymptotically normal. Combination of this result with that in Ling ([ 11 ]) for the stationary case gives the asymptotic normality of the maximum likelihood estimator of ϕ for any ϕ in the real line, with a root- n rate of convergence. This is in contrast to the results for the classical ar(1) model, corresponding to α = 0.