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Covariance-based orthogonality tests for regressors with unknown persistence

  • Katsumi Shimotsu
  • Alex Maynard

This paper develops a new covariance-based test of orthogonality that may beattractive when regressors have roots close or equal to unity. In this case standard regression-based orthogonality tests can suffer from (i) size distortions and (ii) uncertainty regarding the appropriate model in which to frame the alternative hypothesis. The new test has good size and power against a wide range of reasonable alternatives for stationary, non-stationary, and local to unity regressors, while avoiding non-standard limiting distributions, size correction, and unit root pre-tests. Asymptotic results are derived and simulations suggest good small sample performance. As an empirical application, we test for the predictability of stock returns using two persistent regressors, the dividend-price-ratio and short-terminterest rate. The recent literature highlights the role of size distortions in traditional tests using these predictors. On the other hand, while often overturning these rejections, recently employed size-corrected regression-based tests may restrict power to alternatives that become less plausible the more persistent the regressor. The covariance-based tests, which have correct size without restricting power, also show considerably weaker evidence against orthogonality than do traditional regressions. Nevertheless, even allowing for near-unit root behavior, in many cases we still reject orthogonality at long horizons using the dividend yield and at short to medium horizons using the one-month treasury bill rate

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 536.

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Date of creation: 11 Aug 2004
Date of revision:
Handle: RePEc:ecm:nasm04:536
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  1. 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.
  2. Goetzmann, W.N., 1990. "Testing The Predictive Power Of Dividend Yields," Papers fb-_90-12, Columbia - Graduate School of Business.
  3. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
  4. 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.
  5. John Y. Campbell & Robert J. Shiller, 1988. "Stock Prices, Earnings and Expected Dividends," NBER Working Papers 2511, National Bureau of Economic Research, Inc.
  6. Marmer, Vadim, 2009. "Nonlinearity, Nonstationarity, and Spurious Forecasts," working papers vadim_marmer-2009-60, Vancouver School of Economics, revised 03 Nov 2009.
  7. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  8. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, 05.
  9. 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.
  10. John Y. Campbell & Motohiro Yogo, 2003. "Efficient Tests of Stock Return Predictability," NBER Working Papers 10026, National Bureau of Economic Research, Inc.
  11. 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.
  12. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
  13. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-73, February.
  14. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
  15. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  16. Robert J. Shiller & John Y. Campbell, 1986. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Cowles Foundation Discussion Papers 812, Cowles Foundation for Research in Economics, Yale University.
  17. 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.
  18. 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.
  19. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  20. repec:cup:etheor:v:10:y:1994:i:3-4:p:672-700 is not listed on IDEAS
  21. 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.
  22. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  23. Lanne, M., 2000. "Testing the Predictability of Stock Returns," University of Helsinki, Department of Economics 488, Department of Economics.
  24. 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.
  25. 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.
  26. 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.
  27. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Cowles Foundation Discussion Papers 719R, Cowles Foundation for Research in Economics, Yale University.
  28. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  29. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
  30. Yakov Amihud & Clifford Hurvich, 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Econometrics 0412008, EconWPA.
  31. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
  32. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  33. 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.
  34. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  35. Yakov Amihud & Clifford Hurvich & Yi Wang, 2004. "Hypothesis Testing in Predictive Regressions," Finance 0412022, EconWPA.
  36. 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.
  37. Andrew Ang & Geert Bekaert, 2001. "Stock Return Predictability: Is it There?," NBER Working Papers 8207, National Bureau of Economic Research, Inc.
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