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Studies in Nonlinear Dynamics & Econometrics

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Volume 21, Issue 1 (Feb 2017)


A semiparametric nonlinear quantile regression model for financial returns

Krenar Avdulaj
  • Corresponding author
  • Institute of Economic Studies, Charles University in Prague, Opletalova 26, 110 00 Prague, Czech Republic
  • Institute of Information Theory and Automation, The Czech Academy of Sciences, Pod Vodarenskou Vezi 4, 182 00 Prague, Czech Republic
  • Email:
/ Jozef Barunik
  • Institute of Economic Studies, Charles University in Prague, Opletalova 26, 110 00 Prague, Czech Republic
  • Institute of Information Theory and Automation, The Czech Academy of Sciences, Pod Vodarenskou Vezi 4, 182 00 Prague, Czech Republic
Published Online: 2016-06-03 | DOI: https://doi.org/10.1515/snde-2016-0044


Accurately measuring and forecasting value-at-risk (VaR) remains a challenging task at the heart of financial economic theory. Recently, quantile regression models have been used successfully to capture the conditional quantiles of returns and to forecast VaR accurately. In this paper, we further explore nonlinearities in data and propose to couple realized measures with the nonlinear quantile regression framework to explain and forecast the conditional quantiles of financial returns. The nonlinear quantile regression models are implied by the copula specifications and allow us to capture possible nonlinearities, tail dependence, and asymmetries in the conditional quantiles of financial returns. Using high frequency data that covers most liquid US stocks in seven sectors, we provide ample evidence of asymmetric conditional dependence with different levels of dependence, which are characteristic for each industry. The backtesting results of estimated VaR favour our approach.

This article offers supplementary material which is provided at the end of the article.

Keywords: copula quantile regression; realized volatility; value-at-risk

JEL Classification: C14; C32; C58; F37; G32


  • Allen, D. E., A. K. Singh, R. J. Powell, M. McAleer, J. Taylor, and L. Thomas. 2013. “Return-Volatility Relationship: Insights from Linear and Non-Linear Quantile Regression.” Tinbergen Institute Discussion Paper 13–020/III, Amsterdam and Rotterdam. urn:NBN:nl:ui:15–1765/38773.

  • Andersen, T., T. Bollerslev, F. Diebold, and P. Labys. 2003. “Modeling and Forecasting Realized Volatility.” Econometrica 71 (2): 579–625.

  • Berkowitz, J., P. Christoffersen, and D. Pelletier. 2011. “Evaluating Value-at-Risk Models With Desk-Level Data.” Management Science 57 (12): 2213–2227.

  • Bouyé, E. and M. Salmon. 2009. Dynamic Copula Quantile Regressions and Tail Area Dynamic Dependence in Forex Markets.” The European Journal of Finance 15 (7–8): 721–750.

  • Brownlees, C. T., and G. M. Gallo. 2010. “Comparison of Volatility Measures: A Risk Management Perspective.” Journal of Financial Econometrics 8 (1): 29–56.

  • Cappiello, L., B. Gérard, A. Kadareja, and S. Manganelli. 2014. “Measuring Comovements by Regression Quantiles.” Journal of Financial Econometrics 12 (14): 645–678.

  • Chen, X., and Y. Fan. 2006. “Estimation of Copula-Based Semiparametric Time Series Models.” Journal of Econometrics 130 (2): 307–335.

  • Chen, X., R. Koenker, and Z. Xiao. 2009. “Copula-Based Nonlinear Quantile Autoregression.” Econometrics Journal 12: S50–S67. [Crossref]

  • Chernozhukov, V., I. Fernández-Val, and A. Galichon. 2009. Improving Point and Interval Estimators of Monotone Functions by Rearrangement.” Biometrika 96 (3): 559–575.

  • Chernozhukov, V., I. Fernández-Val, and A. Galichon. 2010. “Quantile and Probability Curves Without Crossing.” Econometrica 78 (3): 1093–1125.

  • Clements M. P., A. B. Galvão, and J. H. Kim. 2008. “Quantile Forecasts of Daily Exchange Rate Returns from Forecasts of Realized Volatility.” Journal of Empirical Finance 15: 729–750.

  • Dette, H., and S. Volgushev. 2008. “Non-Crossing Non-Parametric Estimates of Quantile Curves.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70 (3): 609–627.

  • Diebold, F. X., and R. S. Mariano. 2002. “Comparing Predictive Accuracy.” Journal of Business & economic statistics 20 (1): 134–144.

  • Engle, R. F., and S. Manganelli. 2004. “Caviar: Conditional Autoregressive Value at Risk by Regression Quantiles.” Journal of Business & Economic Statistics 22 (4): 367–381.

  • Genest, C., K. Ghoudi, and L.-P. Rivest. 1995. “A Semiparametric Estimation Procedure of Dependence Parameters in Multivariate Families of Distributions.” Biometrika 82 (3): 543–552.

  • Giacomini, R., and I. Komunjer. 2005. “Evaluation and Combination of Conditional Quantile Forecasts.” Journal of Business & Economic Statistics 23 (4): 416–431.

  • Koenker, R. 2004. “Quantile Regression for Longitudinal Data.” Journal of Multivariate Analysis 91 (1): 74–89. Special Issue on Semiparametric and Nonparametric Mixed Models.

  • Koenker, R., and G. Bassett, Jr. 1978. “Regression Quantiles.” Econometrica 46 (1): 33–50.

  • Koenker, R., and B. J. Park. 1996. “An Interior Point Algorithm for Nonlinear Quantile Regression.” Journal of Econometrics 71 (1–2): 265–283.

  • Maheu, J. M., and T. H. McCurdy. 2011. “Do High-Frequency Measures of Volatility Improve Forecasts of Return Distributions?” Journal of Econometrics 160 (1): 69–76. Realized Volatility.

  • Portnoy, S., and R. Koenker. 1997, 11. “The Gaussian Hare and The Laplacian Tortoise: Computability of Squared-Error Versus Absolute-Error Estimators.” Statistical Science 12 (4): 279–300.

  • Xiao, Z. 2009. “Quantile Cointegrating Regression.” Journal of Econometrics 150 (2): 248–260. Recent Development in Financial Econometrics.

  • Žikeš, F., and J. Baruník. 2016. “Semi-Parametric Conditional Quantile Models for Financial Returns and Realized Volatility.” Journal of Financial Econometrics 14 (1): 185–226.

About the article

Published Online: 2016-06-03

Published in Print: 2017-02-01

Citation Information: Studies in Nonlinear Dynamics & Econometrics, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2016-0044. Export Citation

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