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On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle

Published online by Cambridge University Press:  11 February 2009

P. Jeganathan
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Abstract

Some asymptotic properties of the least-squares estimator of the parameters of an AR model of order p, p ≥ 1, are studied when the roots of the characteristic polynomial of the given AR model are on or near the unit circle. Specifically, the convergence in distribution is established and the corresponding limiting random variables are represented in terms of functionals of suitable Brownian motions.

Further, the preceding convergence in distribution is strengthened to that of convergence uniformly over all Borel subsets. It is indicated that the method employed for this purpose has the potential of being applicable in the wider context of obtaining suitable asymptotic expansions of the distributions of leastsquares estimators.

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 3 , September 1991 , pp. 269 - 306
Copyright
Copyright © Cambridge University Press 1991

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