  We propose a class of dynamic vine copula models. This is an extension of
static vine copulas and a generalization of dynamic C-vine and D-vine copulas
studied by Almeida et al (2016) and Goel and Mehra (2019). Within this class,
we allow for time-varying dependence by driving the vine copula parameters with
latent AR(1) processes. This modeling approach is very flexible but estimation
is not straightforward due to the high-dimensional parameter space. We propose
a Bayesian estimation approach, which relies on a novel approximation of the
posterior distribution. This approximation allows to use Markov Chain Monte
Carlo methods, such as elliptical slice sampling, in a sequential way. In
contrast to other Bayesian sequential estimation procedures for vine copula
models as proposed by Gruber and Czado (2015), there is no need to collapse
copula parameters to point estimates before proceeding to the next tree. Thus
more information and uncertainty is propagated from lower to higher trees. A
simulation study shows satisfactory performance of the Bayesian procedure. This
dynamic modeling and inference approach can be applied in various fields, where
static vine copulas have already proven to be successful, including
environmental sciences, medicine and finance. Here we study the dependence
among 21 exchange rates. For comparison we also estimate a static vine copula
model and dynamic C-vine and D-vine copula models. This comparison shows
superior performance of the proposed dynamic vine copula model with respect to
one day ahead forecasting accuracy.
