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We consider the problem of modeling the dependence among many time series. Webuild high dimensional time-varying copula models by combining pair-copulaconstructions (PCC) with stochastic autoregressive copula (SCAR) models tocapture dependence that changes over time. We show how the estimation of thishighly complex model can be broken down into the estimation of a sequence ofbivariate SCAR models, which can be achieved by using the method of simulatedmaximum likelihood. Further, by restricting the conditional dependenceparameter on higher cascades of the PCC to be constant, we can greatly reducethe number of parameters to be estimated without losing much flexibility. Westudy the performance of our estimation method by a large scale Monte Carlosimulation. An application to a large dataset of stock returns of allconstituents of the Dax 30 illustrates the usefulness of the proposed modelclass.

Modeling high dimensional time-varying dependence using D-vine SCAR models