IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v25y2004i1p127-135.html
   My bibliography  Save this article

A small‐sample overlapping variance‐ratio test

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1046/j.0143-9782.2003.01804.x
    Download Restriction: no
    File URL: https://libkey.io/10.1046/j.0143-9782.2003.01804.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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," 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Yamin Ahmad & Ivan Paya, 2014. "Temporal Aggregation of Random Walk Processes and Implications for Asset Prices," Working Papers 14-01, UW-Whitewater, Department of Economics.
    3. 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.
    4. 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.
    5. 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.
    6. Lee, Chun I. & Pan, Ming-Shiun & Liu, Y. Angela, 2001. "On market efficiency of Asian foreign exchange rates: evidence from a joint variance ratio test and technical trading rules," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 11(2), pages 199-214, June.
    7. 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.
    8. Simone Bianco & Roberto Ren'o, 2006. "Unexpected volatility and intraday serial correlation," Papers physics/0610023, arXiv.org.
    9. 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.
    10. Luger, Richard, 2003. "Exact non-parametric tests for a random walk with unknown drift under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 115(2), pages 259-276, August.
    11. Simone Bianco & Roberto Reno, 2009. "Unexpected volatility and intraday serial correlation," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 465-475.
    12. 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.
    13. Daniel, Kent, 2001. "The power and size of mean reversion tests," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 493-535, December.
    14. 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).
    15. Ahmad Yamin S & Paya Ivan, 2020. "Temporal aggregation of random walk processes and implications for economic analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(2), pages 1-20, April.
    16. Cribari-Neto, Francisco, 1996. "On time series econometrics," The Quarterly Review of Economics and Finance, Elsevier, vol. 36(Supplemen), pages 37-60.
    17. Fatas, Antonio, 2000. "Endogenous growth and stochastic trends," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 107-128, February.
    18. Joao Sousa Andrade & Irina Syssoyeva-Masson, 2016. "Investigating the presence of long memory in debt series and its relation with growth," EcoMod2016 9627, EcoMod.
    19. In Choi, 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.
    20. Bley, Jorg, 2011. "Are GCC stock markets predictable?," Emerging Markets Review, Elsevier, vol. 12(3), pages 217-237, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jtsera:v:25:y:2004:i:1:p:127-135. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.