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Predictive regression under various degrees of persistence and robust long-horizon regression

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  • Phillips, Peter C.B.
  • Lee, Ji Hyung

Abstract

The paper proposes a novel inference procedure for long-horizon predictive regression with persistent regressors, allowing the autoregressive roots to lie in a wide vicinity of unity. The invalidity of conventional tests when regressors are persistent has led to a large literature dealing with inference in predictive regressions with local to unity regressors. Magdalinos and Phillips (2009b) recently developed a new framework of extended IV procedures (IVX) that enables robust chi-square testing for a wider class of persistent regressors. We extend this robust procedure to an even wider parameter space in the vicinity of unity and apply the methods to long-horizon predictive regression. Existing methods in this model, which rely on simulated critical values by inverting tests under local to unity conditions, cannot be easily extended beyond the scalar regressor case or to wider autoregressive parametrizations. In contrast, the methods developed here lead to standard chi-square tests, allow for multivariate regressors, and include predictive processes whose roots may lie in a wide vicinity of unity. As such they have many potential applications in predictive regression. In addition to asymptotics under the null hypothesis of no predictability, the paper investigates validity under the alternative, showing how balance in the regression may be achieved through the use of localizing coefficients and developing local asymptotic power properties under such alternatives. These results help to explain some of the empirical difficulties that have been encountered in establishing predictability of stock returns.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 177 (2013)
Issue (Month): 2 ()
Pages: 250-264

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Handle: RePEc:eee:econom:v:177:y:2013:i:2:p:250-264

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Asymptotic theory; Balanced regression; Endogeneity; Instrumentation; IVX methods; Local power; Mild integration; Mildly explosive; Predictive regression; Robustness;

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References

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  1. Kothari, S. P. & Shanken, Jay, 1997. "Book-to-market, dividend yield, and expected market returns: A time-series analysis," Journal of Financial Economics, Elsevier, vol. 44(2), pages 169-203, May.
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  3. 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.
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  7. 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.
  8. Hjalmarsson, Erik, 2011. "New Methods for Inference in Long-Horizon Regressions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(03), pages 815-839, June.
  9. Peter C.B.Phillips & Tassos Magdalinos, 2009. "Econometric Inference in the Vicinity of Unity," Working Papers CoFie-06-2009, Sim Kee Boon Institute for Financial Economics.
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  11. Nikolay Gospodinov, 2009. "A New Look at the Forward Premium Puzzle," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(3), pages 312-338, Summer.
  12. Ioannis Kasparis & Elena Andreou & Peter C. B. Phillips, 2012. "Nonparametric Predictive Regression," University of Cyprus Working Papers in Economics 14-2012, University of Cyprus Department of Economics.
  13. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  14. 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.
  15. Elliott, Graham, 2011. "A control function approach for testing the usefulness of trending variables in forecast models and linear regression," Journal of Econometrics, Elsevier, vol. 164(1), pages 79-91, September.
  16. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
  17. Cochrane, John H., 1991. "Volatility tests and efficient markets : A review essay," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 463-485, June.
  18. 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.
  19. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
  20. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  21. Magdalinos, Tassos & Phillips, Peter C.B., 2009. "Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors," Econometric Theory, Cambridge University Press, vol. 25(02), pages 482-526, April.
  22. 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 1427-44, September.
  23. Amihud, Yakov & Hurvich, Clifford M., 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(04), pages 813-841, December.
  24. Peter C.B. Phillips, 2012. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Cowles Foundation Discussion Papers 1879, Cowles Foundation for Research in Economics, Yale University.
  25. Torous, Walter & Valkanov, Rossen, 2000. "Boundaries of Predictability: Noisy Predictive Regressions," University of California at Los Angeles, Anderson Graduate School of Management qt33p7672z, Anderson Graduate School of Management, UCLA.
  26. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  27. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
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