Backtesting value-at-risk: A GMM duration-based test

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 GMMtest leads to major consequences for the expost evaluation of the risk by regulation authorities. © The Author 2010. Published by Oxford University Press. All rights reserved.