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Biometrika Advance Access originally published online on January 24, 2008
Biometrika 2008 95(1):257-263; doi:10.1093/biomet/asm084
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© 2008 Biometrika Trust

Miscellanea

Asymptotic inference for a nonstationary double AR(1) model

Shiqing Ling and Dong Li

Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong maling{at}ust.hk malidong{at}ust.hk

Received for publication 1 June 2006. Revision received 1 June 2007.

We investigate the nonstationary double AR(1) model,


Formula

where {omega} > 0, {alpha} > 0, the {eta}t are independent standard normal random variables and Elog |{phi} + {eta}t{surd}{alpha}| >= 0. We show that the maximum likelihood estimator of ({phi}, {alpha}) 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 {phi} for any {phi} 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 {alpha} = 0.

Key Words: Asymptotic distribution • Double AR(1) model • Maximum likelihood estimator



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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
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Right arrow Articles by Ling, S.
Right arrow Articles by Li, D.
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