Time varying Hierarchical Archimedean Copulae

There is increasing demand for models of time-varying and non-Gaussian dependencies for mul- tivariate time-series. Available models suffer from the curse of dimensionality or restrictive assumptions on the parameters and the distribution. A promising class of models are the hierarchical Archimedean copulae (HAC) that allow for non-exchangeable and non-Gaussian dependency structures with a small number of parameters. In this paper we develop a novel adaptive estimation technique of the parameters and of the structure of HAC for time-series. The approach relies on a local change point detection procedure and a locally constant HAC approximation. Typical applications are in the financial area but also recently in the spatial analysis of weather parameters. We analyse the time varying dependency structure of stock indices and exchange rates. We find that for stock indices the copula parameter changes dynam- ically but the hierarchical structure is constant over time. Interestingly in our exchange rate example both structure and parameters vary dynamically.