C. Ausin, M. Kalli

In this work, we propose new Bayesian nonparametric copula models that allow for capturing tail dependencies. The main motivation arises from financial time series where it is very common to observe strong dependencies on the tails of the distributions, especially in the lower tails. This phenomenon is usually captured with parametric copula models such as Gumbel or Clayton copulas. However, nonparametric copulas are very scarce in the Bayesian literature and none of the proposed models seems to be able to capture tail dependencies. Our proposal consists of random infinite partitions of unity under the Dirichlet prior. We define a hierarchical prior model over an infinite partition of the unit hypercube. Further, we use a stick-breaking representation to express the model as an infinite mixture of known distributions and implement a Gibbs sampling approach to sample from the posterior. We illustrate the procedure using simulated and real data.

Keywords: Bayesian nonparametrics, copulas, tail dependence.


Bayesian methods
June 7, 2022  4:50 PM
Audiovisual room

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