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

Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes in the dependence structure. Recently, two methods to analyze such changes using copula have been proposed. The first approach only investigates the changes of copula parameters while ignoring the possibility of the changing for the copula family. The other one stresses to inspect any change for copulas by determining the best copula on every subsamples divided by moving-window. However, the width of moving window and the time interval of moving obviously greatly influence the accuracy of the result due to the copula change. In this paper, we first generalize the types of copula change as follows : (1) the changes of parameters while the copula family keeps static ; (2) the changes of copula family. Then, we propose a series of tests based on the conditional pseudo copula and goodness-of-fit (GOF) test to decide the type of change. Eventually, we take the full advantage of the previous methods by avoiding their deficiencies to deal with the changes. Combining the two brilliant ideas, we obtain all information on the changes (such as the change time, the change value of parameter and the change trend) that play the important role in risk management. Moreover, we illustrate our approach with FX spot data for Asian market, which shows that the approach can be practical in the real world as well.