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Estimation and Inference in Predictive Regressions


  • Eiji Kurozumi
  • Kohei Aono


This paper proposes new point estimates for predictive regressions. Our estimates are easily obtained by the least squares and the instrumental variable methods. Our estimates, called the plug-in estimates, have nice asymptotic properties such as median unbiasedness and the approximated normality of the associated t-statistics. In addition, the plug-in estimates are shown to have good finite sample properties via Monte Carlo simulations. Using the new estimates, we investigate U.S. stock returns and find that some variables, which have not been statistically detected as useful predictors in the literature, are able to predict stock returns. Because of their nice properties, our methods complement the existing statistical tests for predictability to investigate the relations between stock returns and economic variables.

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  • Eiji Kurozumi & Kohei Aono, 2011. "Estimation and Inference in Predictive Regressions," Global COE Hi-Stat Discussion Paper Series gd11-192, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:ghsdps:gd11-192

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    References listed on IDEAS

    1. Yamamoto, Taku & Kurozumi, Eiji, 2005. "Lag augmentation in regression models with possibly integrated regressors," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 46(2), pages 159-175, December.
    2. Markku Lanne, 2002. "Testing The Predictability Of Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 407-415, August.
    3. 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.
    4. 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.
    5. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    6. Gregory Mankiw, N. & Shapiro, Matthew D., 1986. "Do we reject too often? : Small sample properties of tests of rational expectations models," Economics Letters, Elsevier, vol. 20(2), pages 139-145.
    7. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    8. Eiji Kurozumi & Taku Yamamoto, 2000. "Modified lag augmented vector autoregressions," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 207-231.
    9. 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.
    10. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    11. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
    12. 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.
    13. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
    14. So, Beong Soo & Shin, Dong Wan, 1999. "Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals," Econometric Theory, Cambridge University Press, vol. 15(02), pages 165-176, April.
    15. 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.
    16. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    17. Choi, In, 1993. "Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications," Econometric Theory, Cambridge University Press, vol. 9(02), pages 263-282, April.
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    More about this item


    unit root; near unit root; bias; median unbiased; stock return;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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