Bücher, AxelPosch, Peter N.Schmidtke, Philipp2018-10-192018-10-192018http://hdl.handle.net/2003/3720110.17877/DE290R-19196We introduce a set of new Value-at-Risk independence backtests by establishing a connection between the independence property of Value-at-Risk forecasts and the extremal index, a general measure of extremal clustering of stationary sequences. We introduce a sequence of relative excess returns whose extremal index has to be estimated. We compare our backtest to both popular and recent competitors using Monte-Carlo simulations and find considerable power in many scenarios. In an applied section we perform realistic out-of-sample forecasts with common forecasting models and discuss advantages and pitfalls of our approach.enDiscussion Paper / SFB823;24/2018VaR backtestingrisk measuresindependenceextremal index310330620working paperValue at RiskStatistischer TestSchätzverfahrenExtremwertstatistik