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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 $({\textstyle{3 \over 4}} - \rho ^2)n^{ - 1} (G_3 (\cdot) - G_1 (\cdot)) + O(n^{ - 2}),$ where |ρ|

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(5), 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. Rustam Ibragimov & Jihyun Kim & Anton Skrobotov, 2020. "New robust inference for predictive regressions," Papers 2006.01191, arXiv.org, revised Mar 2023.
    2. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.
    3. 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.
    4. Noud P.A. van 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. Zongwu Cai & Seong Yeon Chang, 2018. "A New Test In A Predictive Regression with Structural Breaks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201811, University of Kansas, Department of Economics, revised Dec 2018.
    6. Fukang Zhu & Zongwu Cai & Liang Peng, 2014. "Predictive regressions for macroeconomic data," Papers 1404.7642, arXiv.org.
    7. Christis Katsouris, 2023. "Unified Inference for Dynamic Quantile Predictive Regression," Papers 2309.14160, arXiv.org, revised Nov 2023.
    8. 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.
    9. Bingduo Yang & Xiaohui Liu & Liang Peng & Zongwu Cai, 2018. "Unified Tests for a Dynamic Predictive Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201808, University of Kansas, Department of Economics, revised Sep 2018.
    10. Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
    11. Zongwu Cai & Haiqiang Chen & Xiaosai Liao, 2020. "A New Robust Inference for Predictive Quantile Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202002, University of Kansas, Department of Economics, revised Feb 2020.
    12. Liu, Xiaohui & Yang, Bingduo & Cai, Zongwu & Peng, Liang, 2019. "A unified test for predictability of asset returns regardless of properties of predicting variables," Journal of Econometrics, Elsevier, vol. 208(1), pages 141-159.
    13. Kurozumi, Eiji & Aono, Kohei, 2013. "Estimation And Inference In Predictive Regressions," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 54(2), pages 231-250, December.
    14. 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.
    15. 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.
    16. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.

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