Um teste de ajuste com foco no valor em risco condicionado

To verify whether an empirical distribution has a specic theoreticaldistribution, several tests have been used like the Kolmogorov-Smirnov andthe Kuiper tests. These tests try to analyze if all parts of the empiricaldistribution has a specic theoretical shape. But, in a Risk Managementframework, the focus of analysis should be on the tails of thedistributions, since we are interested on the extreme returns of nancialassets. This paper proposes a new goodness-of-t hypothesis test with focuson the tails of the distribution. The new test is based on the ConditionalValue at Risk measure. Then we use Monte Carlo Simulations to assess thepower of the new test with different sample sizes, and then compare with theCrnkovic and Drachman, Kolmogorov-Smirnov and the Kuiper tests. Resultsshowed that the new distance has a better performance than the otherdistances on small samples. We also performed hypothesis tests usingnancial data. We have tested the hypothesis that the empirical distributionhas a Normal, Scaled Student-t, Generalized Hyperbolic, Normal InverseGaussian and Hyperbolic distributions, based on the new distance proposed onthis paper.