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UNIT ROOTS IN WHITE NOISE

Published online by Cambridge University Press:  25 November 2011

Alexei Onatski  and
Harald Uhlig
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Abstract

We show that the empirical distribution of the roots ofthe vector autoregression (VAR) of orderp fitted to Tobservations of a general stationary ornonstationary process converges to the uniformdistribution over the unit circle on the complexplane, when both T andp tend to infinity so that (lnT)/p → 0 andp3/T→ 0. In particular, even if the process is a whitenoise, nearly all roots of the estimated VAR willconverge by absolute value to unity. For fixedp, we derive an asymptoticapproximation to the expected empirical distributionof the estimated roots as T → ∞.The approximation is concentrated in a circularregion in the complex plane for various datagenerating processes and sample sizes.

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Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 3 , June 2012 , pp. 485 - 508
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

We are grateful to the editor, Peter Phillips,the co-editor, Pentti Saikkonen, and two anonymousreferees for excellent, helpful comments.

References

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