Hierarchical Archimedean Copulae over time dependence with applications to Financial Data

In the classical multivariate time series models the residuals are assumed to be normally distributed. However the assumption of normality is rarely consistent with the empirical evidence and leads to possibly incorrect inferences from financial models. The copula theory allows us to extend the classical time series models to nonelliptically distributed residuals. In this paper we analyze the time behavior of hierarchical Archimedean copulas. This class is a generalization of the Archimedean copulas and allows to model more general non-exchangeable dependency structures. In this paper we use hierarchical Archimedean copulae with adaptively estimated time varying parameters and structures for modelling the distribution of returns. We also compare the classical rolling window approach to the local change point detection.