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ON THE ASYMPTOTIC POWER OF THE VARIANCE RATIO TEST

Published online by Cambridge University Press:  31 January 2003

Rohit S. Deo  and
Matthew Richardson
Rohit S. Deo
Affiliation:
New York University
Matthew Richardson
Affiliation:
New York University
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Abstract

The variance-ratio (VR) test statistic, which is based on k-period differences of the data, is commonly used in empirical finance and economics to test the random walk hypothesis. We obtain the asymptotic power function of the VR test statistic when the differencing period k is increasing with the sample size n such that k/n → δ > 0. We show that the test is inconsistent against a variety of mean-reverting alternatives, confirm the result in simulations, and then characterize the functional form of the asymptotic power in terms of δ and these alternatives.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 2 , April 2003 , pp. 231 - 239
Copyright
© 2003 Cambridge University Press

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