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Ols Bias in a Nonstationary Autoregression

Published online by Cambridge University Press:  11 February 2009

Karim M. Abadir
Karim M. Abadir
Affiliation:
The American University in Cairo
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Abstract

An analytical formula is derived to approximate the finite sample bias of the ordinary least-squares (OLS) estimator of the autoregressive parameter when the underlying process has a unit root. It is found that the bias is expressible in terms of parabolic cylinder functions which are easy to compute. Numerical evaluation of the formula reveals that the approximation is very accurate. The derived formula inspires a heuristic approximation, obtained by leastsquares fitting of the asymptotic bias. More importantly, the formula proves analytically that the bias declines at a rate which is slower than the consistency rate, thus explaining some previous simulation findings. A case where the bias increases with the sample size is also given.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 1 , January 1993 , pp. 81 - 93
Copyright
Copyright © Cambridge University Press 1993

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