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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 of the vector autoregression (VAR) of order p fitted to T observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T)/p → 0 and p3/T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed p, we derive an asymptotic approximation to the expected empirical distribution of the estimated roots as T → ∞. The approximation is concentrated in a circular region in the complex plane for various data generating processes and sample sizes.

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 anonymous referees for excellent, helpful comments.

References

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