Goodness-of-Fit Tests for Copulas of Multivariate Time Series

Abstract

The asymptotic behaviour of the empirical copula constructed from residuals of stochastic volatility models is studied. It is shown that if the stochastic volatility matrix is diagonal, then the empirical copula process behaves like if the parameters were known, a remarkable property. However, that is not true if the stochastic volatility is genuinely non-diagonal. Applications for goodness-of-fit and structural change of the dependence between innovations are discussed.

Keywords: goodness-of-fit, time series, dynamic copulas, GARCH models

JEL Classification: C14, C32, C51