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We explore the application of spectral methods in risk management as means ofvalidating VaR models. We propose to replace earlier spectral VaR tests with the testbased on the Anderson-Darling statistic. Based on assumptions relevant to VaR failureanalysis, we experimentally prove that the Anderson-Darling spectral test displaysstrong power to reject inaccurate VaR. Its main advantage over the existing methods isthe combination of two features: the lack of tendency to overreject properly predictedVaR 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 asoutbreaks of financial crises. We confirm this empirically, based on data starting beforethe subprime mortgage crisis, running through the COVID-19 pandemic, until theoutbreak of the RussoUkrainian war. We give a number of examples when this methodrevealed the inaccuracy of VaR predictions not discovered by commonly used tests.We also show that the proposed spectral test never failed at finding the modelsindicated as incorrect by other tests.

Spectral test, Value-at-Risk, VaR test, Anderson-Darling statistic, Financial crisis