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

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

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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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
DOI: 10.1016/j.jeconom.2013.04.011
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  1. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
  2. Peter C. B. Phillips & Jun Yu, 2009. "Dating the Timeline of Financial Bubbles During the Subprime Crisis," Working Papers 18-2009, Singapore Management University, School of Economics.
  3. 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.
  4. 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.
  5. Yakov Amihud & Clifford Hurvich, 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Econometrics 0412008, EconWPA.
  6. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, 02.
  7. 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.
  8. Michael Jansson & Marcelo J. Moreira, 2004. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Harvard Institute of Economic Research Working Papers 2047, Harvard - Institute of Economic Research.
  9. Cochrane, John H., 1991. "Volatility tests and efficient markets : A review essay," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 463-485, June.
  10. 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.
  11. 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.
  12. repec:skb:wpaper:cofie-06-2009 is not listed on IDEAS
  13. 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.
  14. 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.
  15. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
  16. Pitarakis, Jean-Yves & Gonzalo, Jesús, 2010. "Regime specific predictability in predictive regressions," UC3M Working papers. Economics we097844, Universidad Carlos III de Madrid. Departamento de Economía.
  17. 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.
  18. 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.
  19. John Y. Campbell & Motohiro Yogo, 2003. "Efficient Tests of Stock Return Predictability," NBER Working Papers 10026, National Bureau of Economic Research, Inc.
  20. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  21. Liu Wei & Maynard Alex S, 2007. "A New Application of Exact Nonparametric Methods to Long-Horizon Predictability Tests," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(1), pages 163-199, March.
  22. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  23. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  24. 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.
  25. Pesaran, M Hashem & Timmermann, Allan, 1995. " Predictability of Stock Returns: Robustness and Economic Significance," Journal of Finance, American Finance Association, vol. 50(4), pages 1201-28, September.
  26. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  27. Nikolay Gospodinov, 2006. "A New Look at the Forward Premium Puzzle," Working Papers 08009, Concordia University, Department of Economics, revised Dec 2008.
  28. 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.
  29. 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.
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