Asymptotic inference for a nonstationary double AR(1) model

Abstract

We investigate the nonstationary double AR(1) model, y t = Φy t-1 + η t √ (ω + αy 2 t-1 ), where ω > 0, a > 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 (2004) 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 a = 0.