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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 hypothesesabout the autoregressive parameterρ in the stable (a) AR(1) model,(b) AR(1) model with intercept, (c) AR(1) model withintercept and linear trend. The correction is foundexplicitly as a function of ρ. Inthe models with deterministic terms, the correctionfactor is asymmetric in ρ.Furthermore, the Bartlett correction ismonotonically increasing in ρ andtends to infinity when ρ approachesthe stability boundary of + 1. Simulation resultsindicate that the Bartlett corrections are useful incontrolling the size of the likelihood ratiostatistic in small samples, although thesecorrections are not the ultimate panacea.

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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 encouragingremarks and two referees for critical commentsthat have led to a complete revision of thispaper. A third referee is appreciated for drawingattention to the impact of the starting value.Furthermore, helpful comments from Peter Boswijkand participants of the ESEM 2004 meeting (Madrid,Spain) and the UvA-Econometrics seminar(Amsterdam, The Netherlands) are gratefullyacknowledged. All errors remain myresponsibility.

References

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