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

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 VaR forecast validity. Using simple J-statistics based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated with duration based backtesting procedures. In particular, it is among the first to take into account problems induced by the estimation risk in duration-based backtesting tests and to other a sub-sampling approach for robust inference derived from Escanciano and Olmo (2009). An empirical application of the method to Nasdaq returns confirms that using the GMM test has major consequences for the ex-post evaluation of risk by regulation regulatory authorities.