Change analysis of a dynamic copula for measuring dependence in multivariate financial data

This paper proposes a new approach to measure dependences in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes inside the dependence structure. Recently, two methods using copulas have been proposed to analyze such changes. The first approach investigates changes inside copula’s parameters. The second one determines sequence of copulas using moving windows. In this paper we take into account the non stationarity of the data and analyze the impact of (1) time-varying parameters for a copula family, (2) sequence of copulas, on the computations of the VaR and ES measures. We propose some tests based on conditional copulas and goodness-of-fit (GOF) tests to decide the type of change, and further give the corresponding change analysis. We illustrate our approach using Standard & Poor 500 and Nasdaq indices in order to compute risk measures, using the two previous methods.