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The Variance Ratio Statistic At Large Horizons

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Author Info
Chen, Willa W.
Deo, Rohit S.

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Abstract

We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroskedasticity in the data, we obtain the asymptotic distribution of the statistic when the horizon k is increasing with the sample size n but at a slower rate so that k n 0. The test is shown to be consistent against a variety of relevant mean reverting alternatives when k n 0. This is in contrast to the case when k n 0, where the statistic has been recently shown to be inconsistent against such alternatives. Second, we provide and justify a simple power transformation of the statistic that yields almost perfectly normally distributed statistics in finite samples, solving the well-known right skewness problem. Third, we provide a more powerful way of pooling information from different horizons to test for mean reverting alternatives. Monte Carlo simulations illustrate the theoretical improvements provided.The authors thank Bruce Hansen and the referees for useful suggestions and comments that greatly improved the paper. The first author s research was supported by NSF grant DMS-0306726.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 02 (April)
Pages: 206-234
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Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:206-234_06

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  3. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  4. Deo, Rohit S. & Richardson, Matthew, 2003. "On The Asymptotic Power Of The Variance Ratio Test," Econometric Theory, Cambridge University Press, vol. 19(02), pages 231-239, April. [Downloadable!]
  5. Faust, Jon, 1992. "When Are Variance Ratio Tests for Serial Dependence Optimal?," Econometrica, Econometric Society, vol. 60(5), pages 1215-26, September. [Downloadable!] (restricted)
  6. Lo, Andrew W. & MacKinlay, A. Craig, 1989. "The size and power of the variance ratio test in finite samples : A Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 40(2), pages 203-238, February. [Downloadable!] (restricted)
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  7. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April. [Downloadable!] (restricted)
  8. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October. [Downloadable!] (restricted)
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  9. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(1), pages 41-66. [Downloadable!] (restricted)
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  10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  11. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October. [Downloadable!] (restricted)
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