IDEAS home Printed from https://ideas.repec.org/a/jof/jforec/v29y2010i5p467-475.html
   My bibliography  Save this article

The variance ratio and trend stationary model as extensions of a constrained autoregressive model

Author

Listed:
  • Shlomo Zilca

    (Faculty of Management, Tel Aviv University, Tel Aviv, Israel)

Abstract

This paper shows that a constrained autoregressive model that assigns linearly decreasing weights to past observations of a stationary time series has important links to the variance ratio methodology and trend stationary model. It is demonstrated that the proposed autoregressive model is asymptotically related to the variance ratio through the weighting schedules that these two tools use. It is also demonstrated that under a trend stationary time series process the proposed autoregressive model approaches a trend stationary model when the memory of the autoregressive model is increased. These links create a theoretical foundation for tests that confront the random walk model simultaneously against a trend stationary and a variety of short- and long-memory autoregressive alternatives. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:jof:jforec:v:29:y:2010:i:5:p:467-475
    DOI: 10.1002/for.1137
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1002/for.1137
    File Function: Link to full text; subscription required
    Download Restriction: no
    File URL: https://libkey.io/10.1002/for.1137?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. Myung Jig Kim & Charles R. Nelson & Richard Startz, 1991. "Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 515-528.
    2. 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.
    3. Richardson, Matthew, 1993. "Temporary Components of Stock Prices: A Skeptic's View," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 199-207, April.
    4. 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.
    5. 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.
    6. 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.
    7. Kim, Chang-Jin & Nelson, Charles R., 1998. "Testing for mean reversion in heteroskedastic data II: Autoregression tests based on Gibbs-sampling-augmented randomization1," Journal of Empirical Finance, Elsevier, vol. 5(4), pages 385-396, October.
    8. Kim, Chang-Jin & Nelson, Charles R. & Startz, Richard, 1998. "Testing for mean reversion in heteroskedastic data based on Gibbs-sampling-augmented randomization1," Journal of Empirical Finance, Elsevier, vol. 5(2), pages 131-154, June.
    9. Jegadeesh, Narasimhan, 1991. "Seasonality in Stock Price Mean Reversion: Evidence from the U.S. and the U.K," Journal of Finance, American Finance Association, vol. 46(4), pages 1427-1444, September.
    10. Richardson, Matthew P & Smith, Tom, 1994. "A Unified Approach to Testing for Serial Correlation in Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(3), pages 371-399, July.
    11. Richardson, Matthew & Stock, James H., 1989. "Drawing inferences from statistics based on multiyear asset returns," Journal of Financial Economics, Elsevier, vol. 25(2), pages 323-348, December.
    12. McQueen, Grant, 1992. "Long-Horizon Mean-Reverting Stock Prices Revisited," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(1), pages 1-18, March.
    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.
    Full references (including those not matched with items on IDEAS)

    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. Kim, Chang-Jin & Morley, James C. & Nelson, Charles R., 2001. "Does an intertemporal tradeoff between risk and return explain mean reversion in stock prices?," Journal of Empirical Finance, Elsevier, vol. 8(4), pages 403-426, September.
    2. Liam Gallagher, 1999. "A multi-country analysis of the temporary and permanent components of stock prices," Applied Financial Economics, Taylor & Francis Journals, vol. 9(2), pages 129-142.
    3. 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.
    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. John B. Donaldson & Rajnish Mehra, 2021. "Average crossing time: An alternative characterization of mean aversion and reversion," Quantitative Economics, Econometric Society, vol. 12(3), pages 903-944, July.
    6. Daniel, Kent, 2001. "The power and size of mean reversion tests," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 493-535, December.
    7. Liam A. Gallagher & Mark P. Taylor, 2002. "Permanent and Temporary Components of Stock Prices: Evidence from Assessing Macroeconomic Shocks," Southern Economic Journal, John Wiley & Sons, vol. 69(2), pages 345-362, October.
    8. Haitham A. Al-Zoubi & Aktham Maghyereh, 2007. "Stationary Component in Stock Prices: A Reappraisal of Empirical Findings," Multinational Finance Journal, Multinational Finance Journal, vol. 11(3-4), pages 287-322, September.
    9. J. Annaert & W. Van Hyfte, 2006. "Long-Horizon Mean Reversion for the Brussels Stock Exchange: Evidence for the 19th Century," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/376, Ghent University, Faculty of Economics and Business Administration.
    10. Malliaropulos, Dimitrios & Priestley, Richard, 1999. "Mean reversion in Southeast Asian stock markets," Journal of Empirical Finance, Elsevier, vol. 6(4), pages 355-384, October.
    11. Nelson Manuel Areal & Manuel Jose Da Rocha Armada, 2002. "The long-horizon returns behaviour of the Portuguese stock market1," The European Journal of Finance, Taylor & Francis Journals, vol. 8(1), pages 93-122.
    12. 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.
    13. Spierdijk, Laura & Bikker, Jacob A. & van den Hoek, Pieter, 2012. "Mean reversion in international stock markets: An empirical analysis of the 20th century," Journal of International Money and Finance, Elsevier, vol. 31(2), pages 228-249.
    14. 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.
    15. 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.
    16. Graflund, Andreas, 2000. "A Bayesian Inference Approach to Testing Mean Reversion in the Swedish Stock Market," Working Papers 2000:8, Lund University, Department of Economics, revised 30 Jan 2002.
    17. L. Spierdijk & J.A. Bikker, 2012. "Mean Reversion in Stock Prices: Implications for Long-Term Investors," Working Papers 12-07, Utrecht School of Economics.
    18. Eric Hillebrand, 2005. "Mean Reversion Expectations and the 1987 Stock Market Crash: An Empirical Investigation," Finance 0501015, University Library of Munich, Germany.
    19. Shu-Ling Chen & Hyeongwoo Kim, 2011. "Nonlinear Mean Reversion across National Stock Markets: Evidence from Emerging Asian Markets," International Economic Journal, Taylor & Francis Journals, vol. 25(2), pages 239-250.
    20. Tien Foo Sing & Kim Hiang Liow & Wei‐Jin Chan, 2002. "Mean reversion of Singapore property stock prices towards their fundamental values," Journal of Property Investment & Finance, Emerald Group Publishing Limited, vol. 20(4), pages 374-387, August.

    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:jof:jforec:v:29:y:2010:i:5:p:467-475. 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-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

    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.