Asymptotic inference for a nonstationary double AR (1) model

Shiqing Ling () and Dong Li

Biometrika, 2008, vol. 95, issue 1, 257-263

Abstract: We investigate the nonstationary double ar(1) model, where ω > 0, α > 0, the η t are independent standard normal random variables and Elog |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. Copyright 2008, Oxford University Press.

Date: 2008
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