Evaluating Value-at-Risk Forecasts : A New Set of Multivariate Backtests

We propose two new tests for detecting clustering in multivariate Value-at-Risk (VaR) forecasts. First, we consider CUSUM-tests to detect first-order instationarities in the matrix of VaR-violations. Second, we propose x²-tests for detecting cross-sectional and serial dependence in the VaR-forecasts. Moreover, we combine our new backtests with a test of unconditional coverage to yield two new backtests of multivariate conditional coverage. In all cases, a bootstrap approximation is possible, but not mandatory in terms of empirical size and power