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A small‐sample overlapping variance‐ratio test

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  • Y. K. Tse
  • K. W. Ng
  • Xibin Zhang

Abstract

. The null distribution of the overlapping variance‐ratio (OVR) test of the random‐walk hypothesis is known to be downward biased and skewed to the right in small samples. As shown by Lo and MacKinlay (1989), the test under‐rejects the null on the left tail seriously when the sample size is small. This property adversely affects the applicability of the OVR test to macroeconomic time series, which usually have rather small samples. In this paper, we propose a modified overlapping variance‐ratio statistic and derive its exact mean under the normality assumption. We propose to approximate the small‐sample distribution of the modified statistic using a beta distribution that matches the (exact) mean and the (asymptotic) variance. A Monte Carlo experiment shows that the beta approximation performs well in small samples.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:1:p:127-135
    DOI: 10.1046/j.0143-9782.2003.01804.x
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    References listed on IDEAS

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    1. 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.
    2. Campbell, John Y. & Mankiw, N. Gregory, 1989. "International evidence on the persistence of economic fluctuations," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 319-333, March.
    3. Campbell, John Y & Mankiw, N Gregory, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 77(2), pages 111-117, May.
    4. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    5. Cecchetti, Stephen G & Lam, Pok-sang, 1994. "Variance-Ratio Tests: Small-Sample Properties with an Application to International Output Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 177-186, April.
    6. Cogley, Timothy, 1990. "International Evidence on the Size of the Random Walk in Output," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 501-518, June.
    7. 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.
    8. Faust, Jon, 1992. "When Are Variance Ratio Tests for Serial Dependence Optimal?," Econometrica, Econometric Society, vol. 60(5), pages 1215-1226, September.
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    Cited by:

    1. Amelie Charles & Olivier Darne, 2009. "Testing for Random Walk Behavior in Euro Exchange Rates," Economie Internationale, CEPII research center, issue 119, pages 25-45.
    2. 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.
    3. Azad, A.S.M. Sohel, 2009. "Random walk and efficiency tests in the Asia-Pacific foreign exchange markets: Evidence from the post-Asian currency crisis data," Research in International Business and Finance, Elsevier, vol. 23(3), pages 322-338, September.

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