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BARTLETT CORRECTION IN THE STABLE AR(1) MODEL WITH INTERCEPT AND TREND

Published online by Cambridge University Press:  01 June 2009

Noud P.A. van Giersbergen
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Abstract

Bartlett corrections are derived for testing hypotheses about the autoregressive parameter ρ in the stable (a) AR(1) model, (b) AR(1) model with intercept, (c) AR(1) model with intercept and linear trend. The correction is found explicitly as a function of ρ. In the models with deterministic terms, the correction factor is asymmetric in ρ. Furthermore, the Bartlett correction is monotonically increasing in ρ and tends to infinity when ρ approaches the stability boundary of + 1. Simulation results indicate that the Bartlett corrections are useful in controlling the size of the likelihood ratio statistic in small samples, although these corrections are not the ultimate panacea.

Type
Brief Report
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 857 - 872
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

The author thanks a co-editor for encouraging remarks and two referees for critical comments that have led to a complete revision of this paper. A third referee is appreciated for drawing attention to the impact of the starting value. Furthermore, helpful comments from Peter Boswijk and participants of the ESEM 2004 meeting (Madrid, Spain) and the UvA-Econometrics seminar (Amsterdam, The Netherlands) are gratefully acknowledged. All errors remain my responsibility.

References

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