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Backtesting VaR Accuracy: A New Simple Test

Author

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  • Christophe Hurlin

    (LEO - Laboratoire d'économie d'Orleans [2008-2011] - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Sessi Tokpavi

    (LEO - Laboratoire d'économie d'Orleans [2008-2011] - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper proposes a new test of Value at Risk (VaR) validation. Our test exploits the idea that the sequence of VaR violations (Hit function) - taking value 1-α, if there is a violation, and -α otherwise - for a nominal coverage rate α verifies the properties of a martingale difference if the model used to quantify risk is adequate (Berkowitz et al., 2005). More precisely, we use the Multivariate Portmanteau statistic of Li and McLeod (1981) - extension to the multivariate framework of the test of Box and Pierce (1970) - to jointly test the absence of autocorrelation in the vector of Hit sequences for various coverage rates considered as relevant for the management of extreme risks. We show that this shift to a multivariate dimension appreciably improves the power properties of the VaR validation test for reasonable sample sizes.

Suggested Citation

  • Christophe Hurlin & Sessi Tokpavi, 2006. "Backtesting VaR Accuracy: A New Simple Test," Working Papers halshs-00068384, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00068384
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00068384
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    Cited by:

    1. Herwartz, Helmut, 2009. "Exact inference in diagnosing Value-at-Risk estimates -- A Monte Carlo device," Economics Letters, Elsevier, vol. 103(3), pages 160-162, June.
    2. Sajjad Rasoul & Coakley Jerry & Nankervis John C, 2008. "Markov-Switching GARCH Modelling of Value-at-Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-31, September.
    3. Herwartz, Helmut, 2008. "Exact inference in diagnosing value-at-risk estimates: A Monte Carlo device," Economics Working Papers 2008-16, Christian-Albrechts-University of Kiel, Department of Economics.

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