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

AbstractWe consider the problem of modeling the dependence among many time series. We build high dimensionaltime-varying copula models by combining pair-copula constructions (PCC) with stochastic autoregressivecopula (SCAR) models to capture dependence that changes overtime. We show how the estimation of thishighly 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 theconditional dependence parameter on higher cascades of the PCC to be constant, we can greatly reducethe number of parameters to be estimated without losing much flexibility. We study the performanceof our estimation method by a large scale Monte Carlo simulation. An application to a large dataset ofstock returns of all constituents of the Dax 30 illustrates the usefulness of the proposed model class.Keywords: Stock return dependence, time-varying copula, D-vines, efficient importance sampling,sequential estimationJEL Classification: C15, C51, C581. IntroductionThe modeling of multivariate distributions is an important task for risk management and asset al-location problems. Since modeling the conditional mean of financial assets is rather difficult, if notimpossible, much research has focused on modeling conditional volatilities and dependencies. The lit-erature on multivariate GARCH (Bauwens et al. 2006) and stochastic volatility models (Harvey et al.1994, Yu and Meyer 2006) offers many approaches to extend univariate volatility models to multivariate