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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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References

REFERENCES

Campbell, J., A. Lo, & A. MacKinlay (1997) The Econometrics of Financial Markets. Princeton: Princeton University Press.
Campbell, J. & N.G. Mankiw (1987) Are output fluctuations transitory? Quarterly Journal of Economics 102, 857–880.Google Scholar
Chen, W. & R. Deo (2001) On Power Transformations of Linear Combinations of Positive Random Variables to Improve Normality. Working paper, New York University.
Cochrane, J. (1988) How big is the random walk in GNP? Journal of Political Economy 96, 893–920.Google Scholar
Daniel, K. (2001) The power and size of mean reversion tests. Journal of Empirical Finance 8, 493–535.CrossRefGoogle Scholar
Fama, E. & K. French (1988) Permanent and temporary components of stock prices. Journal of Political Economy 96, 246–273.CrossRefGoogle Scholar
Faust, J. (1992) When are variance ratio tests for serial dependence optimal? Econometrica 60, 1215–1226.Google Scholar
Lo, A. & A.C. MacKinlay (1988) Stock market prices do not follow random walks: Evidence from a simple specification test. Review of Financial Studies 1, 41–66.CrossRefGoogle Scholar
Lo, A. & A.C. MacKinlay (1989) The size and power of the variance ratio test in finite samples: A Monte Carlo investigation. Journal of Econometrics 40, 203–238.CrossRefGoogle Scholar
Perron, P. & C. Vodounou (2001) The Variance Ratio Test: An Analysis of Size and Power Based on a Continuous-Time Asymptotic Framework. Working paper, Boston University.
Poterba, J. & L. Summers (1988) Mean reversion in stock returns: Evidence and implications. Journal of Financial Economics 22, 27–60.CrossRefGoogle Scholar
Richardson, M. & T. Smith (1991) Tests of financial models with the presence of overlapping observations. Review of Financial Studies 4, 227–254.CrossRefGoogle Scholar
Richardson, M. & T. Smith (1994) A unified approach to testing for serial correlation in stock returns. Journal of Business 67, 371–399.CrossRefGoogle Scholar
Richardson, M. & J. Stock (1989) Drawing inferences from statistics based on multi-year asset returns. Journal of Financial Economics 25, 323–348.CrossRefGoogle Scholar