A General Multivariate Threshold GARCH Model for Dynamic Correlations

Abstract

We propose a new multivariate DCC-GARCH model that extends existing approaches by admitting multivariate thresholds in conditional volatilities and conditional correlations. Model estimation is numerically feasible in large dimensions and positive semi-definiteness of conditional covariance matrices is naturally ensured by the pure model structure. Conditional thresholds in volatilities and correlations are estimated from the data, together with all other model parameters. We study the performance of our approach in some Monte Carlo simulations, where it is shown that the model is able to fit correctly a GARCH-type dynamics and a complex threshold structure in conditional volatilities and correlations of simulated data. In a real data application to international equity markets, we observe estimated conditional volatilities that are strongly influenced by GARCH-type and multivariate threshold effects. Conditional correlations, instead, are determined by simple threshold structures where no GARCH-type effect could be identified.

Keywords: Multivariate GARCH models, Dynamic conditional correlations, Tree-structured GARCH models, Model confidence set approach

JEL Classification: C12, C13, C51, C53, C61