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When Are Variance Ratio Tests for Serial Dependence Optimal?

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  • Faust, Jon

Abstract

This paper considers a class of statistics that can be written as the ratio of the sample variance of a filtered time series to the sample variance of the original series. Any such statistic is shown to be optimal under normality for testing a null of white noise against some class of serially dependent alternatives. A simple characterization of the alternative class is provided. The results are used to show that a variance ratio test for mean reversion is an optimal test and to illustrate the forms of mean reversion it is best at detecting. Copyright 1992 by The Econometric Society.

Suggested Citation

  • Faust, Jon, 1992. "When Are Variance Ratio Tests for Serial Dependence Optimal?," Econometrica, Econometric Society, vol. 60(5), pages 1215-1226, September.
  • Handle: RePEc:ecm:emetrp:v:60:y:1992:i:5:p:1215-26
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    Cited by:

    1. Lunde A. & Timmermann A., 2004. "Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 253-273, July.
    2. Nityanda Sarkar & Debabrata Mukhopadhyay, 2005. "Testing Predictability and Nonlinear Dependence in the Indian Stock Market," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 41(6), pages 7-44, November.
    3. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
    4. Nityanda Sarkar & Debabrata Mukhopadhyay, 2005. "Testing Predictability and Nonlinear Dependence in the Indian Stock Market," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 41(6), pages 7-44, November.
    5. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate Variance Ratio Statistics," Cambridge Working Papers in Economics 1459, Faculty of Economics, University of Cambridge.
    6. Graflund, Andreas, 2001. "Some Time Serial Properties of the Swedish Real Estate Stock Market, 1939-1998," Working Papers 2001:8, Lund University, Department of Economics.
    7. Chen, Willa W. & Deo, Rohit S., 2006. "The Variance Ratio Statistic At Large Horizons," Econometric Theory, Cambridge University Press, vol. 22(02), pages 206-234, April.
    8. Amélie Charles & Olivier Darné, 2009. "Variance-Ratio Tests Of Random Walk: An Overview," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 503-527, July.
    9. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into Multivariate Variance Ratio Statistics and their application to Stock Market Predictability," Cambridge Working Papers in Economics 1552, Faculty of Economics, University of Cambridge.
    10. Simone Bianco & Roberto Ren'o, 2006. "Unexpected volatility and intraday serial correlation," Papers physics/0610023, arXiv.org.
    11. Campbell, John Y., 2001. "Why long horizons? A study of power against persistent alternatives," Journal of Empirical Finance, Elsevier, pages 459-491.
    12. Shlomo Zilca, 2010. "The variance ratio and trend stationary model as extensions of a constrained autoregressive model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(5), pages 467-475.
    13. Ronen, Tavy, 1998. "Trading structure and overnight information: A natural experiment from the Tel-Aviv Stock Exchange," Journal of Banking & Finance, Elsevier, vol. 22(5), pages 489-512, May.
    14. Benjamin Miranda Tabak & Eduardo José Araújo Lima, 2002. "The Effects of the Brazilian ADRs Program on Domestic Market Efficiency," Working Papers Series 43, Central Bank of Brazil, Research Department.
    15. Diebold, Francis X. & Lindner, Peter, 1996. "Fractional integration and interval prediction," Economics Letters, Elsevier, vol. 50(3), pages 305-313, March.
    16. Daniel, Kent, 2001. "The power and size of mean reversion tests," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 493-535, December.
    17. Wang, Yuming & Ma, Jinpeng, 2014. "Excess volatility and the cross-section of stock returns," The North American Journal of Economics and Finance, Elsevier, vol. 27(C), pages 1-16.
    18. Shively, Philip A., 2002. "An exact invariant variance ratio test," Economics Letters, Elsevier, vol. 75(3), pages 347-353, May.
    19. Deo, Rohit S. & Chen, Willa W., 2003. "The Variance Ratio Statistic at Large Horizons," Papers 2004,04, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    20. Choi, In, 1999. "Testing the Random Walk Hypothesis for Real Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 293-308, May-June.

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