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Estimation and Inference in Predictive Regressions

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  • Eiji Kurozumi
  • Kohei Aono

Abstract

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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File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd11-192.pdf
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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd11-192.

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Date of creation: May 2011
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Handle: RePEc:hst:ghsdps:gd11-192

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

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  1. Eiji Kurozumi & Taku Yamamoto, 2000. "Modified lag augmented vector autoregressions," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 207-231.
  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. 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.
  4. 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.
  5. Lanne, M., 2000. "Testing the Predictability of Stock Returns," University of Helsinki, Department of Economics 488, Department of Economics.
  6. John Y. Campbell & Motohiro Yogo, 2002. "Efficient Tests of Stock Return Predictability," Harvard Institute of Economic Research Working Papers 1972, Harvard - Institute of Economic Research.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  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. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  16. 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.
  17. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
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