Multivariate Distributional Tests in Risk Management: An Empirical Characteristic Function Approach

Abstract

With the purpose of identifying appropriate testing procedures for multivariate distributional forecasts, in this paper we compare the power of two versions of multivariate goodness-of-fit tests based on the Empirical Characteristic Function (ECF) in detecting deviations of the true distribution of the data from the forecast. Various Monte Carlo experiments carried out for dimensions up to 16 suggest the superiority of the continuous version of the test over the discrete one, in terms of both computational feasibility and statistical properties. The applicability of this testing procedure to the evaluation of density forecasts of financial asset returns generated in the context of risk management and Value at Risk models is carefully investigated.

Keywords: Multivariate density forecasting, distributional tests, empirical characteristic function, Value at Risk, mixture of normal.

JEL Classification: C12, C15, C53