A general multivariate threshold GARCH model with dynamic conditional correlations

We introduce a new multivariate GARCH model with multivariate thresholds in conditional correlations and develop a two-step estimation procedure that is feasible in large dimensional applications. Optimal threshold functions are estimated endogenously from the data, and the model conditional covariance matrix is ensured to be positive definite. We study the empirical performance of our model in two applications using US stock and bond market data. The conditional volatility of stock returns exhibits GARCH and threshold structures, but the conditional correlation dynamics depend on piecewise constant thresholds only. We estimate both threshold and GARCH structures in the conditional correlations of stock and government bond returns. In both applications our model has, in terms of statistical and economic significance, higher forecasting power than several other multivariate GARCH models for conditional correlations.