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

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  • Bertrand Candelon
  • Gilbert Colletaz
  • Christophe Hurlin
  • Sessi Tokpavi

Abstract

This paper proposes a new duration-based backtesting procedure for value-at-risk (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. An empirical application for Nasdaq returns confirms that using GMM test leads to major consequences for the expost evaluation of the risk by regulation authorities. JEL: C22, C52, G28 Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 9 (2011)
Issue (Month): 2 (Spring)
Pages: 314-343

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Handle: RePEc:oup:jfinec:v:9:y:2011:i:2:p:314-343

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References

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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  2. 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.).
  3. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques.
  4. Christian Bontemps & Nour Meddahi, 2012. "Testing distributional assumptions: A GMM aproach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 978-1012, 09.
  5. Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO.
  6. Escanciano, J. C. & Olmo, J., 2007. "Estimation risk effects on backtesting for parametric value-at-risk models," Working Papers 07/11, Department of Economics, City University London.
  7. Jean-Marie Dufour, 2005. "Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics," CIRANO Working Papers 2005s-02, CIRANO.
  8. 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.
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Citations

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Cited by:
  1. Asai, M. & Caporin, M. & McAleer, M.J., 2012. "Forecasting Value-at-Risk Using Block Structure Multivariate Stochastic Volatility Models," Econometric Institute Research Papers EI 2012-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. Ludwig, Alexander, 2013. "Sovereign risk contagion in the Eurozone: a time-varying coefficient approach," MPRA Paper 52340, University Library of Munich, Germany.
  3. Elena‐Ivona Dumitrescu & Christophe Hurlin & Jaouad Madkour, 2013. "Testing Interval Forecasts: A GMM‐Based Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(2), pages 97-110, 03.
  4. Metiu, Norbert, 2012. "Sovereign risk contagion in the Eurozone," Economics Letters, Elsevier, vol. 117(1), pages 35-38.
  5. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Asymmetry and Long Memory in Volatility Modelling," Documentos del Instituto Complutense de Análisis Económico 2011-29, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
  6. Bontemps, Christian, 2013. "Moment-Based Tests for Discrete Distributions," IDEI Working Papers 772, Institut d'Économie Industrielle (IDEI), Toulouse.
  7. Araújo Santos, P. & Fraga Alves, M.I., 2012. "A new class of independence tests for interval forecasts evaluation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3366-3380.
  8. Christophe Hurlin & Christophe Pérignon, 2012. "Margin Backtesting," Working Papers halshs-00746274, HAL.
  9. Candelon, Bertrand & Joëts, Marc & Tokpavi, Sessi, 2013. "Testing for Granger causality in distribution tails: An application to oil markets integration," Economic Modelling, Elsevier, vol. 31(C), pages 276-285.
  10. Elena-Ivona Dumitrescu & Christophe Hurlin & Vinson Pham, 2012. "Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests," Working Papers halshs-00671658, HAL.
  11. Bertrand Candelon & Marc Joëts & Sessi Tokpavi, 2012. "Testing for crude oil markets globalization during extreme price movements," EconomiX Working Papers 2012-28, University of Paris West - Nanterre la Défense, EconomiX.
  12. Evers, Corinna & Rohde, Johannes, 2014. "Model Risk in Backtesting Risk Measures," Hannover Economic Papers (HEP) dp-529, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  13. Denisa Georgiana Banulescu & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2013. "High-Frequency Risk Measures," Working Papers halshs-00859456, HAL.
  14. Leccadito, Arturo & Boffelli, Simona & Urga, Giovanni, 2014. "Evaluating the accuracy of value-at-risk forecasts: New multilevel tests," International Journal of Forecasting, Elsevier, vol. 30(2), pages 206-216.
  15. El Bouhadi, Abdelhamid & Achibane, Khalid, 2009. "The Predictive Power of Conditional Models: What Lessons to Draw with Financial Crisis in the Case of Pre-Emerging Capital Markets?," MPRA Paper 19482, University Library of Munich, Germany.

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