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Backtesting Value-at-Risk: A GMM Duration-Based Test

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Author Info
Christophe Hurlin () (Laboratoire d'Economie d'Orléans - Université d'Orléans - CNRS : FRE2783)
Gilbert Colletaz (Laboratoire d'Economie d'Orléans - Université d'Orléans - CNRS : FRE2783)
Sessi Tokpavi () (Laboratoire d'Economie d'Orléans - Université d'Orléans - CNRS : FRE2783)
Bertrand Candelon (Laboratoire d'Economie d'Orléans - Université d'Orléans - CNRS : FRE2783)

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Abstract

This paper proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e. the geometric distribution) is applied to the case of the VaR forecasts validity. Using simple J-statistic based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated to duration based backtesting procedures. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis (Christoffersen, 1998). Third, feasibility of the tests is improved. Fourth, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. An empirical application for Nasdaq returns confirms that using GMM test leads to major consequences for the ex-post evaluation of the risk by regulation authorities. Without any doubt, this paper provides a strong support for the empirical application of duration-based tests for VaR forecasts.

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Paper provided by HAL in its series Working Papers with number halshs-00329495_v1.

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Date of creation: 10 Oct 2008
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Handle: RePEc:hal:wpaper:halshs-00329495_v1

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Related research
Keywords: Value-at-Risk; backtesting; GMM; duration-based test;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
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  1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January. [Downloadable!] (restricted)
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August. [Downloadable!] (restricted)
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  4. J. Carlos Escanciano & Jose Olmo, 2007. "Estimation risk effects on backtesting for parametric value-at-risk models," City University Economics Discussion Papers 07/11, Department of Economics, City University, London. [Downloadable!]
  5. Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO. [Downloadable!]
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  6. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  7. 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.
  8. 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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