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Estimation and inference in semiparametric quantile factor models. (English) Zbl 1471.62332

Summary: We consider a semiparametric quantile factor panel model that allows observed stock-specific characteristics to affect stock returns in a nonlinear time-varying way, extending [G. Connor et al., Econometrica 80, No. 2, 713–754 (2012; Zbl 1274.91485)] to the quantile restriction case. We propose a sieve-based estimation methodology that is easy to implement. We provide tools for inference that are robust to the existence of moments and to the form of weak cross-sectional dependence in the idiosyncratic error term. We apply our method to daily stock return data where we find significant evidence of nonlinearity in many of the characteristic exposure curves.

MSC:

62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics

Citations:

Zbl 1274.91485
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References:

[1] Babu, G. J., Strong representations for LAD estimators in linear models, Probab. Theory Related Fields, 83, 547-558 (1989) · Zbl 0665.62033
[2] Bai, J.; Li, K., Statistical analysis of Factor Models of High Dimension, Ann. Statist., 40, 436-465 (2012) · Zbl 1246.62144
[3] Bai, J.; Ng, S., Determining the number of Factors in Approximate Factor Models, Econometrica, 70, 191-221 (2002) · Zbl 1103.91399
[4] Bellman, R. E., Adaptive Control Processes (1961), Princeton University Press: Princeton University Press Princeton, N.J. · Zbl 0103.12901
[5] de Boor, C., (A Practical Guide to Splines. A Practical Guide to Splines, Applied Mathematical Sciences, vol. 27 (2001), Springer: Springer New York) · Zbl 0987.65015
[6] Bradley, B. O.; Taqqu, M. S., Financial risk and heavy tails, (Handbook of Heavy Tailed Distributions in Finance (2003)), 35-103
[7] Bryzgalova, S., Spurious Factors in Linear Asset Pricing ModelsWorking Paper (2015)
[8] Cai, T.; Liu, W., Adaptive thresholding for sparse Covariance Matrix Estimation, J. Amer. Statist. Assoc., 106, 672-684 (2011) · Zbl 1232.62086
[9] Chen, X., Penalized Sieve Estimation and Inference of Semi-Nonparametric Dynamic Models: A Selective ReviewCowles Foundation Discussion Paper No. 1804 (2011)
[10] Conley, T. G., GMM estimation with Cross-Sectional dependence, J. Econometrics, 92, 1-45 (1999) · Zbl 0944.62117
[11] Connor, G.; Hagmann, M.; Linton, O., Efficient semiparametric estimation of the Fama-French Model and Extensions, Econometrica, 80, 713-754 (2012) · Zbl 1274.91485
[12] Connor, G.; Korajczyk, R. A., A test for the number of factors in an Approximate Factor Model, J. Finance, 48, 1263-1288 (1993)
[13] Dong, C.; Gao, J.; Peng, B., Semiparametric Single-Index panel data models with Cross-Sectional dependence, J. Econometrics, 188, 301-312 (2015) · Zbl 1337.62256
[14] Fama, E. F.; French, K. R., The Cross-Section of Expected Stock returns, J. Finance, 47, 427-465 (1992)
[15] Fama, E. F.; French, K. R., Common risk factors in the returns to Stocks and bonds, J. Financ. Econ., 33, 3-56 (1993) · Zbl 1131.91335
[16] Fan, J.; Liao, Y.; Micheva, M., Large covariance estimation by thresholding principal orthogonal complements (with Discussion), J. R. Stat. Soc. Ser. B Stat. Methodol., 75, 603-680 (2013) · Zbl 1411.62138
[17] Fan, J.; Liao, Y.; Wang, W., Projected principal Component Analysis in Factor Models, Ann. Statist., 44, 219-254 (2016) · Zbl 1331.62295
[18] Gao, J.; Lu, Z.; Tjøstheim, D., Estimation in Semiparametric Spatial Regression, Ann. Statist., 34, 1395-1435 (2006) · Zbl 1113.62048
[19] Gorski, J.; Pfeuffer, F.; Klamroth, K., Biconvex sets and optimization with biconvex functions: a survey and extensions, Math. Methods Oper. Res., 66, 373-407 (2007) · Zbl 1146.90495
[20] G. W., Bassett.; Koenker, R.; Kordas, G., Pessimistic portfolio allocation and choquet expected utility, J. Financ. Econ., 2, 477-492 (2004)
[21] He, X.; Shi, P., Bivariate tensor-product B-splines in a partly linear model, J. Multivariate Anal., 58, 162-181 (1996) · Zbl 0865.62027
[22] Horowitz, J. L.; Lee, S., Nonparametric estimation of an Additive Quantile Regression model, J. Amer. Statist. Assoc., 100, 1238-1249 (2005) · Zbl 1117.62355
[23] Horowitz, J. L.; Mammen, E., ORacle-Efficient nonparametric estimation of an additive model with an unknown Link Function, Econometric Theory, 27, 582-608 (2011) · Zbl 1218.62034
[24] Kiefer, N. M.; Vogelsang, T. J., Heteroskedasticity-Autocorrelation Robust Standard Errors using the Bartlett Kernel without truncation, Econometrica, 70, 2093-2095 (2002) · Zbl 1101.62367
[25] Kiefer, N. M.; Vogelsang, T. J., A new Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests, Econometric Theory, 21, 1130-1164 (2005) · Zbl 1082.62040
[26] Koenker, R.; Machado, J., Goodness of fite and related inference processes for quantile regression, J. Amer. Statist. Assoc., 94, 1296-1310 (1999) · Zbl 0998.62041
[27] Lam, C.; Yao, Q., Factor modeling for high-dimensional time series: Inference for the Number of Factors, Ann. Statist., 40, 694-726 (2012) · Zbl 1273.62214
[28] Lee, J.; Robinson, P. M., Series estimation under Cross-Sectional Dependence, J. Econometrics, 190, 1-17 (2016) · Zbl 1419.62515
[29] Li, Q.; Cheng, G.; Fan, J.; Wang, Y., Embracing blessing of Dimensionality in Factor Models, J. Amer. Statist. Assoc., 113, 380-389 (2018) · Zbl 1398.62137
[30] Ma, S.; Song, Q.; Wang, L., Simultaneous variable selection and estimation in Semiparametric Modelling of Longitudinal/clustered Data, Bernoulli, 19, 252-274 (2013) · Zbl 1259.62021
[31] Ma, S.; Yang, L., Spline-Backfitted Kernel Smoothing of partially linear additive model, J. Statist. Plann. Inference, 14, 204-219 (2011) · Zbl 1197.62130
[32] Mammen, E., Bootstrap and wild bootstrap for high dimensional linear models, Ann. Statist., 21, 255-285 (1993) · Zbl 0771.62032
[33] Merlevède, E.; Peligrad, F. M.; Rio, E., Bernstein inequality and moderate deviations under Strong Mixing Conditions IMS Collections, (High Dimensional Probability V: The Luminy Volume 5 (2009)), 273-292 · Zbl 1243.60019
[34] Powell, J. L., Estimation of Monotonic Regression Models under quantile restrictions, (Barnett, W.; Powell, J.; Tauchen, G., Nonparametric and Semiparametric Models in Econometrics (1991), Cambridge University Press: Cambridge University Press Cambridge) · Zbl 0754.62023
[35] Robinson, P. M.; Thawornkaiwong, S., Statistical inference on Regression with Spatial Dependence, J. Econometrics, 167, 521-542 (2012) · Zbl 1441.62852
[36] Xue, P. M.; Yang, S., Additive coefficient modeling via polynomial spline, Statist. Sinica, 16, 1423-1446 (2006) · Zbl 1109.62030
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