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The Variance Ratio Statistic at large Horizons

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  • Willa Chen

    (Texas A&M University)

  • Rohit Deo

    (New york University)

Abstract

We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroscedasticity 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 ¨ƒÂ>0, where the statistic has been recently shown to be inconsistent against such alternatives. Secondly, we provide and justify a simple power transformation of the statistic which yields almost perfectly normally distributed statistics in finite samples, solving the well known right skewness problem. Thirdly, 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.

Suggested Citation

  • Willa Chen & Rohit Deo, 2005. "The Variance Ratio Statistic at large Horizons," Econometrics 0501003, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0501003
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    References listed on IDEAS

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    1. 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, Society for Financial Studies, vol. 1(1), pages 41-66.
    2. 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.
    3. 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 246-273, April.
    4. 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.
    5. John Y. Campbell & N. Gregory Mankiw, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 857-880.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    8. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    9. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    10. Matthew Richardson & James H. Stock, 1990. "Drawing Inferences From Statistics Based on Multi-Year Asset Returns," NBER Working Papers 3335, National Bureau of Economic Research, Inc.
    11. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    12. 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.
    13. Faust, Jon, 1992. "When Are Variance Ratio Tests for Serial Dependence Optimal?," Econometrica, Econometric Society, vol. 60(5), pages 1215-1226, September.
    14. 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.
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    Cited by:

    1. Amélie Charles & Olivier Darné & Jessica Fouilloux, 2010. "Testing the Martingale Difference Hypothesis in the EU ETS Markets for the CO2 Emission Allowances: Evidence from Phase I and Phase II," Working Papers hal-00473727, HAL.
    2. Charles, Amélie & Darné, Olivier & Fouilloux, Jessica, 2011. "Testing the martingale difference hypothesis in CO2 emission allowances," Economic Modelling, Elsevier, vol. 28(1), pages 27-35.
    3. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2012. "Exchange-rate return predictability and the adaptive markets hypothesis: Evidence from major foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1607-1626.
    4. Anoop S. KUMAR & Bandi KAMAIAH, 2016. "Efficiency, non-linearity and chaos: evidences from BRICS foreign exchange markets," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(1(606), S), pages 103-118, Spring.
    5. Regis Augusto Ely, 2011. "Returns Predictability and Stock Market Efficiency in Brazil," Brazilian Review of Finance, Brazilian Society of Finance, vol. 9(4), pages 571-584.
    6. 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.
    7. S. Anoop Kumar & Bandi Kamaiah, 2014. "Efficient Market Hypothesis: Some Evidences from Emerging European Forex Markets," Romanian Economic Journal, Department of International Business and Economics from the Academy of Economic Studies Bucharest, vol. 17(52), pages 27-44, June.
    8. Verheyden, Tim & De Moor, Lieven & Van den Bossche, Filip, 2015. "Towards a new framework on efficient markets," Research in International Business and Finance, Elsevier, vol. 34(C), pages 294-308.
    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. Muneer Shaik & S. Maheswaran, 2017. "Market Efficiency of ASEAN Stock Markets," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 7(2), pages 109-122, February.
    11. Peter C. B. Phillips & Sainan Jin, 2014. "Testing the Martingale Hypothesis," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 537-554, October.
    12. Amelie Charles & Olivier Darne, 2009. "Testing for Random Walk Behavior in Euro Exchange Rates," Economie Internationale, CEPII research center, issue 119, pages 25-45.
    13. Kim, Jae H., 2009. "Automatic variance ratio test under conditional heteroskedasticity," Finance Research Letters, Elsevier, vol. 6(3), pages 179-185, September.
    14. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Risk prediction management and weak form market efficiency in Eurozone financial crisis," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 384-393.
    15. Sasikumar, Anoop, 2011. "Testing for weak form market efficiency in Indian foreign exchange market," MPRA Paper 37071, University Library of Munich, Germany.
    16. Chen, Min & Zhu, Ke, 2014. "Sign-based specification tests for martingale difference with conditional heteroscedasity," MPRA Paper 56347, University Library of Munich, Germany.
    17. Roberto Ortiz & Mauricio Contreras & Marcelo Villena, 2015. "On the Efficient Market Hypothesis of Stock Market Indexes: The Role of Non-synchronous Trading and Portfolio Effects," Papers 1510.03926, arXiv.org.

    More about this item

    Keywords

    Mean reversion; frequency domain; power transformations;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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