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

This paper proposes a new approach to measure the dependence 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 the changes of copula's parameters. The second one tests the changes of copulas by determining the best copulas using moving windows. In this paper we take into account the non stationarity of the data and analyze : (1) the changes of parameters while the copula family keeps static ; (2) the changes of copula family. We propose a series of 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 with Standard & Poor 500 and Nasdaq indices, and provide dynamic risk measures.