  We consider the problem of modeling the dependence among many time series. We
build high dimensional time-varying copula models by combining pair-copula
constructions (PCC) with stochastic autoregressive copula (SCAR) models to
capture dependence that changes over time. We show how the estimation of this
highly complex model can be broken down into the estimation of a sequence of
bivariate SCAR models, which can be achieved by using the method of simulated
maximum likelihood. Further, by restricting the conditional dependence
parameter on higher cascades of the PCC to be constant, we can greatly reduce
the number of parameters to be estimated without losing much flexibility. We
study the performance of our estimation method by a large scale Monte Carlo
simulation. An application to a large dataset of stock returns of all
constituents of the Dax 30 illustrates the usefulness of the proposed model
class.
