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

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

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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File URL: http://hdl.handle.net/10.1093/jjfinec/nbq025
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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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  1. Juan Carlos Escanciano & Jose Olmo, 2007. "Backtesting Parametric Value-at-Risk with Estimation Risk," Caepr Working Papers 2007-005_updated, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  2. 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.
  3. 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.
  4. Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO.
  5. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques.
  6. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  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. 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.
  9. 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.).
  10. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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