A spectral approach to evaluating VaR forecasts: stock market evidence from the subprime mortgage crisis, through COVID-19, to the Russo–Ukrainian war

We explore the application of spectral methods in risk management as means of validating VaR models. We propose to replace earlier spectral VaR tests with the test based on the Anderson–Darling statistic. Based on assumptions relevant to VaR failure analysis, we experimentally prove that the Anderson–Darling spectral test displays strong power to reject inaccurate VaR. Its main advantage over the existing methods is the combination of two features: the lack of tendency to overreject properly predicted VaR and high sensitivity to limited evidence of incorrectness in VaR predictions. Thus, this test may play an important role in times of change in volatility dynamics, such as outbreaks of financial crises. We confirm this empirically, based on data starting before the subprime mortgage crisis, running through the COVID-19 pandemic, until the outbreak of the Russo–Ukrainian war. We give a number of examples when this method revealed the inaccuracy of VaR predictions not discovered by com- monly used tests. We also show that the proposed spectral test never failed at finding the models indicated as incorrect by other tests.