Realized covariance models with time-varying parameters and spillover effects

A realized covariance model specifies a dynamic process for a conditional covariance matrix of daily asset returns as a function of past realized variances and covariances. We propose parsimonious parameterizations enabling a spillover effect in the conditional variance equations, and a specific nonlinear, time-varying, effect of the lagged realized covariance between each asset pair on the corresponding conditional covariance. We introduce these parameterizations in four classes of realized covariance models. In an application to the components of the Dow Jones index, we find that the extended models improve the fit of their less flexible scalar versions and show a good out-of-sample forecast performance, in particular for short forecast horizons.