Spectral density tests in VaR failure correlation analysis
Spectral density tests in VaR failure correlation analysis

Summary/Abstract: The paper presents application of the spectral theory, developed primarily in physics, to risk analysis in economics. The aim of the paper was to evaluate statistical properties of spectral density-based VaR tests based on various test statistics and to compare them to the popular Christoffersen’s Markov test. Test assessment included their size and power. The analysis of the test properties was preceded by the overview of spectral theory methods proposed in the literature for testing VaR failure correlation. The statistical properties of the considered tests were evaluated through the Monte Carlo method. The study showed that the spectral test approach outperformed the Markov test in terms of the test power, however, the asymptotic distributions of the test statistics did not ensure the proper size of the tests. The comparison of the four considered spectral test statistics indicated the superiority of the test based on the Cramer-von-Mises statistic over all other tests.

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