This paper 1 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 the VaR forecasts validity. Using simple J-statistic based on the moments de…ned by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated to duration based backtesting procedures. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis (Christo¤ersen, 1998). Third, feasibility of the tests is improved. Fourth, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. An empirical application for Nasdaq returns con…rms that using GMM test leads to major consequences for the ex-post evaluation of the risk by regulation authorities. Without any doubt, this paper provides a strong support for the empirical application of duration-based tests for VaR forecasts.

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This article introduces a kernel-based nonparametric inferential procedure to test for Granger causality in distribution. This test is a multivariate extension of the kernel-based Granger causality test in tail event.The main advantage of this test is its ability to examine a large number of lags, with higher-order lags discounted. In addition, our test is highly flexible because it can be used to identify Granger causality in specific regions on the distribution supports, such as the center or tails. We prove that the test converges asymptotically to a standard Gaussian distribution under the null hypothesis and thus is free of parameter estimation uncertainty. Monte Carlo simulations illustrate the excellent small sample size and power properties of the test. This new test is applied to a set of European stock markets to analyze spillovers during the recent European crisis and to distinguish contagion from interdependence effects.