We 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.

中文翻译：

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使用极值指数进行风险价值回测*

通过在风险价值预测的独立性与极值指数之间建立联系，我们引入了一组新的风险独立性回测，这是固定序列极值聚类的一种通用度量。我们引入一系列相对超额收益，其极值指数必须估计。我们使用蒙特卡洛模拟将我们的回测与流行和最近的竞争对手进行比较，并在许多情况下发现了强大的功能。在应用部分中，我们将使用常见的预测模型执行实际的样本外预测，并讨论该方法的优点和陷阱。