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Specification Tests of Parametric Dynamic Conditional Quantiles

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Author Info
Juan Carlos Escanciano () (Indiana University Bloomington)
Carlos Velasco () (Universidad Carlos III de Madrid)

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Abstract

This article proposes omnibus specification tests of parametric dynamic quantile regression models. Contrary to the existing procedures, we allow for a flexible and general specification framework where a possibly continuum of quantiles are simultaneously specified. This is the case for many econometric applications for both time series and cross section data which require a global diagnostic tool. We study the asymptotic distribution of the test statistics under fairly weak conditions on the serial dependence in the underlying data generating process. It turns out that the asymptotic null distribution depends on the data generating process and the hypothesized model. We propose a subsampling procedure for approximating the asymptotic critical values of the tests. An appealing property of the proposed tests is that they do not require estimation of the non-parametric (conditional) sparsity function. A Monte Carlo study compares the proposed tests and shows that the asymptotic results provide good approximations for small sample sizes. Finally, an application to some European stock indexes provides evidence that our methodology is a powerful and flexible alternative to standard backtesting procedures in evaluating market risk by using information from a range of quantiles in the lower tail of returns.

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Paper provided by Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington in its series Caepr Working Papers with number 2008-021.

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Length: 33 pages
Date of creation: Aug 2008
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Handle: RePEc:inu:caeprp:2008-021

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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  1. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September. [Downloadable!] (restricted)
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  2. He X. & Hu F., 2002. "Markov Chain Marginal Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 783-795, September. [Downloadable!] (restricted)
  3. Herman J. Bierens & Donna K. Ginther, 2001. "Integrated Conditional Moment testing of quantile regression models," Empirical Economics, Springer, vol. 26(1), pages 307-324. [Downloadable!] (restricted)
  4. Bilias, Yannis & Chen, Songnian & Ying, Zhiliang, 2000. "Simple resampling methods for censored regression quantiles," Journal of Econometrics, Elsevier, vol. 99(2), pages 373-386, December. [Downloadable!] (restricted)
  5. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive density and conditional confidence interval accuracy tests," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 187-228. [Downloadable!] (restricted)
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  6. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September. [Downloadable!] (restricted)
  7. Juan Carlos Escanciano & Silvia Mayoral, 2008. "Semiparametric estimation of dynamic conditional expected shortfall models," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 1(2), pages 106-120, January. [Downloadable!] (restricted)
  8. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
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  9. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  10. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283. [Downloadable!] (restricted)
  11. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September. [Downloadable!] (restricted)
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  12. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  13. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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  14. Joshua Angrist & Victor Chernozhukov & Ivan Fernandez-Val, 2004. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," NBER Working Papers 10428, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  15. Escanciano, J. Carlos, 2009. "On The Lack Of Power Of Omnibus Specification Tests," Econometric Theory, Cambridge University Press, vol. 25(01), pages 162-194, February. [Downloadable!]
  16. Horowitz J.L. & Spokoiny V.G., 2002. "An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 822-835, September. [Downloadable!] (restricted)
  17. Jim Albrecht & Aico van Vuuren & Susan Vroman, 2007. "Counterfactual Distributions with Sample Selection Adjustments: Econometric Theory and an Application to the Netherlands," Working Papers gueconwpa~07-07-06, Georgetown University, Department of Economics. [Downloadable!]
  18. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December. [Downloadable!] (restricted)
  19. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    Other versions:
  20. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  21. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February. [Downloadable!]
  22. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2005. "Evaluating Value-at-Risk models with desk-level data," Working Paper Series 010, North Carolina State University, Department of Economics, revised Dec 2006. [Downloadable!]
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  23. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July. [Downloadable!] (restricted)
  24. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October. [Downloadable!] (restricted)
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