Asymptotic inference for a nonstationary double AR(1) model

Authors: Ling, Shiqing; Li, Dong

Source: Biometrika, Volume 95, Number 1, 6 March 2008 , pp. 257-263(7)

Buy & download fulltext article:

Price: $35.78 plus tax (Refund Policy)

Abstract:

We investigate the nonstationary double ar(1) model, <disp-formula><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="asm084ueq1.gif"/></disp-formula> where > 0, > 0, the _t are independent standard normal random variables and Elog _t 0. We show that the maximum likelihood estimator of (,) is consistent and asymptotically normal. Combination of this result with that in Ling ([<xref ref-type="bibr" rid="R11">11</xref>]) for the stationary case gives the asymptotic normality of the maximum likelihood estimator of for any 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 0.

Keywords: Asymptotic distribution; Double AR(1) model; Maximum likelihood estimator

Document Type: Research article

DOI: http://dx.doi.org/10.1093/biomet/asm084

Publication date: 2008-03-06