IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence

  • Maynard, Alex
  • Shimotsu, Katsumi

This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard predictive regression tests can suffer from well-documented size distortion. Moreover, under the alternative hypothesis, they force the dependent variable to share the same order of integration as the predictor, whereas in practice the dependent variable often appears stationary and the predictor may be near-nonstationary. By contrast, the new test does not enforce the same orders of integration and is therefore capable of detecting a rich set of alternatives to orthogonality that are excluded by the standard predictive regression model. Moreover, the test statistic has a standard normal limit distribution for both unit root and local-to-unity conditioning variables, without prior knowledge of the local-to-unity parameter. If the conditioning variable is stationary, the test remains conservative and consistent. Simulations suggest good small-sample performance. As an empirical application, we test for the predictability of stock returns using two persistent predictors, the dividend-price ratio and short-term interest rate.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://journals.cambridge.org/abstract_S0266466608090038
File Function: link to article abstract page
Download Restriction: no

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 25 (2009)
Issue (Month): 01 (February)
Pages: 63-116

as
in new window

Handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:63-116_09
Contact details of provider: Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK
Web page: http://journals.cambridge.org/jid_ECT
Email:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Marmer, Vadim, 2009. "Nonlinearity, Nonstationarity, and Spurious Forecasts," Microeconomics.ca working papers vadim_marmer-2009-60, Vancouver School of Economics, revised 03 Nov 2009.
  2. Michael Jansson & Marcelo J. Moreira, 2004. "Optimal Inference in Regression Models with Nearly Integrated Regressors," NBER Technical Working Papers 0303, National Bureau of Economic Research, Inc.
  3. Campbell, B. & Dufour, J.M., 1994. "Excat Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," Cahiers de recherche 9407, Universite de Montreal, Departement de sciences economiques.
  4. James H. Stock, 1991. "Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series," NBER Technical Working Papers 0105, National Bureau of Economic Research, Inc.
  5. repec:cup:etheor:v:10:y:1994:i:3-4:p:672-700 is not listed on IDEAS
  6. Wright, Jonathan H, 2000. "Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 211-22, April.
  7. Campbell, John & Shiller, Robert, 1988. "Stock Prices, Earnings, and Expected Dividends," Scholarly Articles 3224293, Harvard University Department of Economics.
  8. Goetzman, W.N. & Jorion, P., 1992. "Testing the Predictive Power of Dividend Yields," Papers 93-03, Columbia - Graduate School of Business.
  9. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
  10. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  11. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Cowles Foundation Discussion Papers 719R, Cowles Foundation for Research in Economics, Yale University.
  12. N. Gregory Mankiw & Matthew D. Shapiro, 1985. "Do We Reject Too Often? Small Sample Properties of Tests of Rational Expectations Models," NBER Technical Working Papers 0051, National Bureau of Economic Research, Inc.
  13. Wolf, Michael, 2000. "Stock Returns and Dividend Yields Revisited: A New Way to Look at an Old Problem," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 18-30, January.
  14. Toda, Hiro Y. & Yamamoto, Taku, 1995. "Statistical inference in vector autoregressions with possibly integrated processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 225-250.
  15. Markku Lanne, 2002. "Testing The Predictability Of Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 407-415, August.
  16. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  17. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
  18. Yakov Amihud & Clifford Hurvich, 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Econometrics 0412008, EconWPA.
  19. Andrew Ang & Geert Bekaert, 2001. "Stock Return Predictability: Is it There?," NBER Working Papers 8207, National Bureau of Economic Research, Inc.
  20. Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation for Research in Economics, Yale University.
  21. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  22. Graham Elliott & James H. Stock, 1992. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," NBER Technical Working Papers 0122, National Bureau of Economic Research, Inc.
  23. Saikkonen, Pentti & L├╝tkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
  24. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  25. Yakov Amihud & Clifford Hurvich & Yi Wang, 2004. "Hypothesis Testing in Predictive Regressions," Finance 0412022, EconWPA.
  26. John Y. Campbell & Motohiro Yogo, 2002. "Efficient Tests of Stock Return Predictability," Harvard Institute of Economic Research Working Papers 1972, Harvard - Institute of Economic Research.
  27. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-86.
  28. Rudebusch, Glenn D, 1992. "Trends and Random Walks in Macroeconomic Time Series: A Re-examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 661-80, August.
  29. 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 246-73, April.
  30. Nelson, Charles R & Kim, Myung J, 1993. " Predictable Stock Returns: The Role of Small Sample Bias," Journal of Finance, American Finance Association, vol. 48(2), pages 641-61, June.
  31. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  32. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
  33. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
  34. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
  35. Walter Torous & Rossen Valkanov & Shu Yan, 2004. "On Predicting Stock Returns with Nearly Integrated Explanatory Variables," The Journal of Business, University of Chicago Press, vol. 77(4), pages 937-966, October.
  36. Alex Maynard, 2006. "The forward premium anomaly: statistical artefact or economic puzzle? New evidence from robust tests," Canadian Journal of Economics, Canadian Economics Association, vol. 39(4), pages 1244-1281, November.
  37. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:63-116_09. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.