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Bias Reduction And Likelihood-Based Almost Exactly Sized Hypothesis Testing In Predictive Regressions Using The Restricted Likelihood

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  • Chen, Willa W.
  • Deo, Rohit S.

Abstract

Difficulties with inference in predictive regressions are generally attributed to strong persistence in the predictor series. We show that the major source of the problem is actually the nuisance intercept parameter, and we propose basing inference on the restricted likelihood, which is free of such nuisance location parameters and also possesses small curvature, making it suitable for inference. The bias of the restricted maximum likelihood (REML) estimates is shown to be approximately 50% less than that of the ordinary least squares (OLS) estimates near the unit root, without loss of efficiency. The error in the chi-square approximation to the distribution of the REML-based likelihood ratio test (RLRT) for no predictability is shown to be null where | ρ | G (·) is the cumulative distribution function (c.d.f.) of a null random variable. This very small error, free of the autoregressive (AR) parameter, suggests that the RLRT for predictability has very good size properties even when the regressor has strong persistence. The Bartlett-corrected RLRT achieves an O ( n −2 ) error. Power under local alternatives is obtained, and extensions to more general univariate regressors and vector AR(1) regressors, where OLS may no longer be asymptotically efficient, are provided. In simulations the RLRT maintains size well, is robust to nonnormal errors, and has uniformly higher power than the Jansson and Moreira (2006, Econometrica 74, 681–714) test with gains that can be substantial. The Campbell and Yogo (2006, Journal of Financial Econometrics 81, 27–60) Bonferroni Q test is found to have size distortions and can be significantly oversized.

Suggested Citation

  • Chen, Willa W. & Deo, Rohit S., 2009. "Bias Reduction And Likelihood-Based Almost Exactly Sized Hypothesis Testing In Predictive Regressions Using The Restricted Likelihood," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1143-1179, October.
  • Handle: RePEc:cup:etheor:v:25:y:2009:i:05:p:1143-1179_09
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    Cited by:

    1. Fukang Zhu & Zongwu Cai & Liang Peng, 2014. "Predictive regressions for macroeconomic data," Papers 1404.7642, arXiv.org.
    2. Amihud, Yakov & Hurvich, Clifford M. & Wang, Yi, 2010. "Predictive regression with order-p autoregressive predictors," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 513-525, June.
    3. Peter C.B. Phillips & Ye Chen, "undated". "Restricted Likelihood Ratio Tests in Predictive Regression," Cowles Foundation Discussion Papers 1968, Cowles Foundation for Research in Economics, Yale University.
    4. Noud P.A. Giersbergen, 2013. "Bartlett correction in the stable second-order autoregressive model with intercept and trend," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 482-498, November.
    5. Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
    6. Adrian Austin & Swarna Dutt, 2015. "Exchange Rates and Fundamentals: A New Look at the Evidence on Long-Horizon Predictability," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 43(1), pages 147-159, March.
    7. Willa W. Chen & Rohit S. Deo, 2009. "The restricted likelihood ratio test at the boundary in autoregressive series," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 618-630, November.

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