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

Abstract

We propose two new tests for detecting clustering in multivariate Value-at-Risk (VaR) forecasts. First, we consider CUSUM-tests to detect non-constant expectations in the matrix of VaR-violations. Second, we propose χ2-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. Results from a simulation study underline the usefulness of our new backtests for controlling portfolio risks across a bank’s business lines. In an empirical study, we show how our multivariate backtests can be employed by regulators to backtest a banking system.