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FINITE-SAMPLE SIZE CONTROL OF IVX-BASED TESTS IN PREDICTIVE REGRESSIONS

Published online by Cambridge University Press:  10 August 2020

Mehdi Hosseinkouchack  and
Matei Demetrescu
Mehdi Hosseinkouchack*
Affiliation:
University of Mannheim
Matei Demetrescu
Affiliation:
Christian-Albrechts-University of Kiel
*
Address correspondence to Mehdi Hosseinkouchack, University of Mannheim, L7, 3-5, 68161 Mannheim, Germany; e-mail: [email protected].
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Abstract

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In predictive regressions with variables of unknown persistence, the use of extended IV (IVX) instruments leads to asymptotically valid inference. Under highly persistent regressors, the standard normal or chi-squared limiting distributions for the usual t and Wald statistics may, however, differ markedly from the actual finite-sample distributions which exhibit in particular noncentrality. Convergence to the limiting distributions is shown to occur at a rate depending on the choice of the IVX tuning parameters and can be very slow in practice. A characterization of the leading higher-order terms of the t statistic is provided for the simple regression case, which motivates finite-sample corrections. Monte Carlo simulations confirm the usefulness of the proposed methods.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 4 , August 2021 , pp. 769 - 793
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

The authors would like to thank three anonymous referees, the Co-Editor (Giuseppe Cavaliere), as well as Karim Abadir and Uwe Hassler for very useful comments. Demetrescu gratefully acknowledges the support of the German Research Foundation (DFG) through the project DE 1617/4-2.

References

REFERENCES

Ang, A. & Bekaert, G. (2007) Return predictability: Is it there? Review of Financial Studies 20(3), 651–707.CrossRefGoogle Scholar
Breitung, J. & Demetrescu, M. (2015) Instrumental variable and variable addition based inference in predictive regressions. Journal of Econometrics 187(1), 358–375.CrossRefGoogle Scholar
Campbell, J.Y. & Yogo, M. (2006) Efficient tests of stock return predictability. Journal of Financial Economics 81(1), 27–60.CrossRefGoogle Scholar
Camponovo, L. (2015) Differencing transformations and inference in predictive regression models. Econometric Theory 31(6), 1331–1358.CrossRefGoogle Scholar
Cavaliere, G., Rahbek, A., & Taylor, A.M.R. (2010) Testing for co-integration in vector autoregressions with non-stationary volatility. Journal of Econometrics 158(1), 7–24.CrossRefGoogle Scholar
Demetrescu, M., Georgiev, I., Rodrigues, P.M.M., & Taylor, A.M.R. (2020) Testing for episodic predictability in stock returns. Journal of Econometrics, forthcoming.CrossRefGoogle Scholar
Demetrescu, M. & Rodrigues, P.M.M. (2016) Residual-Augmented IVX Predictive Regression. Working paper 5/2016, Banco de Portugal.Google Scholar
Elliott, G. & Stock, J.H. (1994) Inference in time series regression when the order of integration of a regressor is unknown. Econometric Theory 10(3–4), 672–700.CrossRefGoogle Scholar
Everaert, G. (2013) Orthogonal to backward mean transformation for dynamic panel data models. The Econometrics Journal 16(2), 179–221.CrossRefGoogle Scholar
Gonzalo, J. & Pitarakis, J.-Y. (2012) Regime-specific predictability in predictive regressions. Journal of Business & Economic Statistics 30(2), 229–241.CrossRefGoogle Scholar
Jansson, M. & Moreira, M.J. (2006) Optimal inference in regression models with nearly integrated regressors. Econometrica 74(3), 681–714.CrossRefGoogle Scholar
Kostakis, A., Magdalinos, T., & Stamatogiannis, M.P. (2015) Robust econometric inference for stock return predictability. Review of Financial Studies 28(5), 1506–1553.CrossRefGoogle Scholar
Magdalinos, T. & Phillips, P.C.B. (2009) Limit theory for cointegrated systems with moderately integrated and moderately explosive regressors. Econometric Theory 25(2), 482–526.CrossRefGoogle Scholar
Maynard, A. & Shimotsu, K. (2009) Covariance-based orthogonality tests for regressors with unknown persistence. Econometric Theory 25(1), 63–116.CrossRefGoogle Scholar
Nickell, S. (1981) Biases in dynamic models with fixed effects. Econometrica 49(6), 1417–1426.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Towards a unified asymptotic theory for autoregression. Biometrika 74(3), 535–547.CrossRefGoogle Scholar
Phillips, P.C.B. (2015) Pitfalls and possibilities in predictive regression. Journal of Financial Econometrics 13(3), 521–555.CrossRefGoogle Scholar
Phillips, P.C.B. & Lee, J.H. (2013) Predictive regression under various degrees of persistence and robust long-horizon regression. Journal of Econometrics 177(2), 250–264.CrossRefGoogle Scholar
Phillips, P.C.B. & Magdalinos, T. (2007) Limit theory for moderate deviations from a unit root. Journal of Econometrics 136(1), 115–130.CrossRefGoogle Scholar
Phillips, P.C.B. & Magdalinos, T. (2009) Econometric Inference in the Vicinity of Unity. CoFie Working Paper 7, Singapore Management University.Google Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20(2), 971–1001.CrossRefGoogle Scholar
Shin, D.W. & So, B.S. (2001) Recursive mean adjustment for unit root tests. Journal of Time Series Analysis 22(5), 595–612.CrossRefGoogle Scholar
So, B.S. & Shin, D.W. (1999) Recursive mean adjustment in time-series inferences. Statistics & Probability Letters 43(1), 65–73.CrossRefGoogle Scholar
Stambaugh, R.F. (1999) Predictive regressions. Journal of Financial Economics 54(3), 375–421.CrossRefGoogle Scholar
Westerlund, J., Karabiyik, H., & Narayan, P. (2017) Testing for predictability in panels with general predictors. Journal of Applied Econometrics 32(3), 554–574.CrossRefGoogle Scholar
Yang, B., Long, W., Peng, L., & Cai, Z. (2020) Testing the predictability of US housing price index returns based on an IVX-AR model. Journal of the American Statistical Association, forthcoming.CrossRefGoogle Scholar
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