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COMPLETE SUBSET AVERAGING FOR QUANTILE REGRESSIONS

Published online by Cambridge University Press:  13 August 2021

Ji Hyung Lee  and
Youngki Shin
Ji Hyung Lee
Affiliation:
University of Illinois
Youngki Shin
Affiliation:
McMaster University
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Abstract

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We propose a novel conditional quantile prediction method based on complete subset averaging (CSA) for quantile regressions. All models under consideration are potentially misspecified, and the dimension of regressors goes to infinity as the sample size increases. Since we average over the complete subsets, the number of models is much larger than the usual model averaging method which adopts sophisticated weighting schemes. We propose to use an equal weight but select the proper size of the complete subset based on the leave-one-out cross-validation method. Building upon the theory of Lu and Su (2015, Journal of Econometrics 188, 40–58), we investigate the large sample properties of CSA and show the asymptotic optimality in the sense of Li (1987, Annals of Statistics 15, 958–975) We check the finite sample performance via Monte Carlo simulations and empirical applications.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 1 , February 2023 , pp. 146 - 188
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 (https://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), 2021. Published by Cambridge University Press

Footnotes

We would like to thank the Editor, Peter Phillips, the Co-Editor, Arthur Lewbel, and three anonymous referees for helpful comments and suggestions, which have led to substantial improvements. We would also like to thank Xun Lu and Liangjun Su for helpful discussion and sharing their codes. Shin is grateful for partial support by the Social Sciences and Humanities Research Council of Canada (SSHRC-435-2018-0275). This work was made possible by the facilities of WestGrid (www.westgrid.ca) and Compute Canada (www.computecanada.ca).

References

REFERENCES

Adrian, T., Boyarchenko, N., & Giannone, D. (2019) Vulnerable growth. American Economic Review 109(4), 1263–1289.CrossRefGoogle Scholar
Ando, T. & Li, K.-C. (2014) A model-averaging approach for high-dimensional regression. Journal of the American Statistical Association 109(505), 254–265.CrossRefGoogle Scholar
Angrist, J., Chernozhukov, V., & Fernández-Val, I. (2006) Quantile regression under misspecification, with an application to the US wage structure. Econometrica 74(2), 539–563.CrossRefGoogle Scholar
Belloni, A. & Chernozhukov, V. (2011) ℓ 1-penalized quantile regression in high-dimensional sparse models. Annals of Statistics 39(1), 82–130.CrossRefGoogle Scholar
Bhatia, K.T., Vecchi, G.A., Knutson, T.R., Murakami, H., Kossin, J., Dixon, K.W., & Whitlock, C.E. (2019) Recent increases in tropical cyclone intensification rates. Nature Communications 10(1), 1–9.CrossRefGoogle ScholarPubMed
Breiman, L. (1996) Bagging predictors. Machine Learning 24(2), 123–140.CrossRefGoogle Scholar
Buchinsky, M. (1998) The dynamics of changes in the female wage distribution in the USA: A quantile regression approach. Journal of Applied Econometrics 13(1), 1–30.3.0.CO;2-A>CrossRefGoogle Scholar
Campbell, J.Y. & Thompson, S.B. (2007) Predicting excess stock returns out of sample: Can anything beat the historical average? The Review of Financial Studies 21(4), 1509–1531.CrossRefGoogle Scholar
Claeskens, G., Magnus, J.R., Vasnev, A.L., & Wang, W. (2016) The forecast combination puzzle: A simple theoretical explanation. International Journal of Forecasting 32(3), 754–762.CrossRefGoogle Scholar
Clemen, R.T. (1989) Combining forecasts: A review and annotated bibliography. International Journal of Forecasting 5(4), 559–583.CrossRefGoogle Scholar
Donald, S.G. & Newey, W.K. (2001) Choosing the number of instruments. Econometrica 69(5), 1161–1191.CrossRefGoogle Scholar
Duffie, D. & Pan, J. (1997) An overview of value at risk. Journal of Derivatives 4(3), 7–49.CrossRefGoogle Scholar
Elliott, G. (2011) Averaging and the optimal combination of forecasts. Manuscript, Department of Economics, University of California, San Diego.Google Scholar
Elliott, G., Gargano, A., & Timmermann, A. (2013) Complete subset regressions. Journal of Econometrics 177(2), 357–373.CrossRefGoogle Scholar
Elliott, G., Gargano, A., & Timmermann, A. (2015) Complete subset regressions with large-dimensional sets of predictors. Journal of Economic Dynamics and Control 54, 86–110.CrossRefGoogle Scholar
Fan, R. & Lee, J.H. (2019) Predictive quantile regressions under persistence and conditional heteroskedasticity. Journal of Econometrics 213(1), 261–280.CrossRefGoogle Scholar
Fazekas, I. & Klesov, O. (2001) A general approach to the strong law of large numbers. Theory of Probability and Its Applications 45(3), 436–449.CrossRefGoogle Scholar
Hansen, B.E. (2007) Least squares model averaging. Econometrica 75(4), 1175–1189.CrossRefGoogle Scholar
Hansen, B.E. & Racine, J.S. (2012) Jackknife model averaging. Journal of Econometrics 167(1), 38–46.CrossRefGoogle Scholar
Hirano, K. & Wright, J.H. (2021) Analyzing cross-validation for forecasting with structural instability. Journal of Econometrics, forthcoming.Google Scholar
Koenker, R. (2005) Quantile Regression. Econometric Society Monographs, vol. 38. Cambridge University Press.CrossRefGoogle Scholar
Koenker, R. & Bassett, G. (1978) Regression quantiles. Econometrica 46(1), 33–50.CrossRefGoogle Scholar
Komunjer, I. (2013). Quantile prediction. In Elliot, G. and Timmerman, A. (eds.), Handbook of Economic Forecasting, vol. 2, pp. 961–994. Elsevier.Google Scholar
Kuersteiner, G. & Okui, R. (2010) Constructing optimal instruments by first-stage prediction averaging. Econometrica 78(2), 697–718.Google Scholar
Lee, J.H. (2016) Predictive quantile regression with persistent covariates: IVX-QR approach. Journal of Econometrics 192(1), 105–118.CrossRefGoogle Scholar
Lee, S. and Shin, Y. (2021) Complete subset averaging with many instruments. The Econometrics Journal, 24(2), 290–314.CrossRefGoogle Scholar
Li, K.-C. (1987) Asymptotic optimality for ${C}_p$ , ${C}_L$ , cross-validation and generalized cross-validation: Discrete index set. Annals of Statistics 15(3), 958–975.CrossRefGoogle Scholar
Lu, X. & Su, L. (2015) Jackknife model averaging for quantile regressions. Journal of Econometrics 188(1), 40–58.CrossRefGoogle Scholar
Meinshausen, N. (2006) Quantile regression forests. Journal of Machine Learning Research 7(35), 983–999.Google Scholar
Meligkotsidou, L., Panopoulou, E., Vrontos, I.D., & Vrontos, S.D. (2019) Quantile forecast combinations in realised volatility prediction. Journal of the Operational Research Society 70(10), 1720–1733.CrossRefGoogle Scholar
Meligkotsidou, L., Panopoulou, E., Vrontos, I.D., & Vrontos, S.D. (2021) Out-of-sample equity premium prediction: A complete subset quantile regression approach. The European Journal of Finance 27(1–2), 110–135.CrossRefGoogle Scholar
Phillips, P.C. (2015) Halbert White Jr. memorial JFEC lecture: Pitfalls and possibilities in predictive regression. Journal of Financial Econometrics 13(3), 521–555.CrossRefGoogle Scholar
Portnoy, S. (1984) Asymptotic behavior of $m$ -estimators of $p$ regression parameters when ${p}^2/ n$ is large. I. Consistency. Annals of Statistics 12(4), 1298–1309.CrossRefGoogle Scholar
Portnoy, S. (1985) Asymptotic behavior of m estimators of p regression parameters when p 2/n is large; II. Normal approximation. Annals of Statistics 13(4), 1403–1417.CrossRefGoogle Scholar
Rapach, D.E., Strauss, J.K., & Zhou, G. (2010) Out-of-sample equity premium prediction: Combination forecasts and links to the real economy. The Review of Financial Studies 23(2), 821–862.CrossRefGoogle Scholar
Rice, J. (1984) Bandwidth choice for nonparametric regression. Annals of Statistics 12(4), 1215–1230.CrossRefGoogle Scholar
Shibata, R. (1981) An optimal selection of regression variables. Biometrika 68(1), 45–54.CrossRefGoogle Scholar
Shibata, R. (1982) Amendments and corrections: An optimal selection of regression variables. Biometrika 69(2), 492–492.CrossRefGoogle Scholar
Smith, J. & Wallis, K.F. (2009) A simple explanation of the forecast combination puzzle. Oxford Bulletin of Economics and Statistics 71(3), 331–355.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2004) Combination forecasts of output growth in a seven-country data set. Journal of Forecasting 23(6), 405–430.CrossRefGoogle Scholar