On the influence of autocorrelation and GARCH-effects on goodness-of-fit tests for copulas

Abstract

Knowing the multivariate stochastic dependence between random variables is of crucial importance for many finance applications. To check the adequacy of copula assumptions by which stochastic dependencies can be described, goodness-of-fit (gof) tests have to be carried out. These tests require (serially) independent and identically distributed (i.i.d.) data as input. Due to autocorrelations and time-varying conditional volatilities, this prerequisite is usually not fulfilled by financial market returns. Within a simulation study, we analyze the influence of these violations of the i.i.d.-prerequisite on the rejection rates of gof tests. We find that in many cases the rejection rates are significantly different for non-i.i.d. data input than for adequately filtered data input. This finding questions the conclusions of early empirical studies applying gof tests for copulas to data without adequately filtering it before. Only in the majority of those constellations that in general yield very low rejection rates, no significant differences have been revealed.