Asymptotic inference for a nonstationary double <sc>AR</sc>(1) model
We investigate the nonstationary double <sc>ar(1)</sc> model, <disp-formula><graphic xlink:href="asm084ueq1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></disp-formula> where ω > 0, α > 0, the η<sub>t</sub> are independent standard normal random variables and Elog |φ + η<sub>t</sub>√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 <sc>ar(1)</sc> model, corresponding to α = 0. Copyright 2008, Oxford University Press.
