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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.

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  • 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. Benjamin Miranda Tabak, 2003. "The random walk hypothesis and the behaviour of foreign capital portfolio flows: the Brazilian stock market case," Applied Financial Economics, Taylor & Francis Journals, vol. 13(5), pages 369-378.
    2. Sibanjan Mishra, 2019. "Testing Martingale Hypothesis Using Variance Ratio Tests: Evidence from High-frequency Data of NCDEX Soya Bean Futures," Global Business Review, International Management Institute, vol. 20(6), pages 1407-1422, December.
    3. 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.
    4. John P. Miller & Paul Newbold, 1995. "A GENERALIZED VARIANCE RATIO TEST OF ARIMA (p, 1, q) MODEL SPECIFICATION," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 403-413, July.
    5. 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.
    6. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate variance ratio statistics," CeMMAP working papers CWP29/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Campbell, John Y., 2001. "Why long horizons? A study of power against persistent alternatives," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 459-491, December.
    8. 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.
    9. 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.
    10. 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.
    11. Simone Bianco & Roberto Reno, 2009. "Unexpected volatility and intraday serial correlation," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 465-475.
    12. Daniel, Kent, 2001. "The power and size of mean reversion tests," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 493-535, December.
    13. 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.
    14. Shively, Philip A., 2002. "An exact invariant variance ratio test," Economics Letters, Elsevier, vol. 75(3), pages 347-353, May.
    15. 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.
    16. 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).
    17. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into multivariate variance ratio statistics and their application to stock market predictability," CeMMAP working papers CWP13/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
    19. Chen, Willa W. & Deo, Rohit S., 2006. "The Variance Ratio Statistic At Large Horizons," Econometric Theory, Cambridge University Press, vol. 22(2), pages 206-234, April.
    20. Mohanty, Sunil K. & Mishra, Sibanjan, 2020. "Regulatory reform and market efficiency: The case of Indian agricultural commodity futures markets," Research in International Business and Finance, Elsevier, vol. 52(C).
    21. Simone Bianco & Roberto Ren'o, 2006. "Unexpected volatility and intraday serial correlation," Papers physics/0610023, arXiv.org.
    22. 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.
    23. Patrick A. Groenendijk & André Lucas & Casper G. de Vries, 1998. "A Hybrid Joint Moment Ratio Test for Financial Time Series," Tinbergen Institute Discussion Papers 98-104/2, Tinbergen Institute.
    24. Diebold, Francis X. & Lindner, Peter, 1996. "Fractional integration and interval prediction," Economics Letters, Elsevier, vol. 50(3), pages 305-313, March.
    25. Y. K. Tse & K. W. Ng & Xibin Zhang, 2004. "A small‐sample overlapping variance‐ratio test," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 127-135, January.

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