In this paper we propose a new model for forecasting discrete high-frequency bi-variate conditional densities and covariance.
The model is composed of two marginals using a modified Skellam distribution and a dynamic conditional Gaussian copula. The dynamics of both the volatilities and the correlation are modelled through state space models with a seasonality factor, which permits the measurement of the intraday seasonality for the covariance. We also estimate a Score Driven model following Koopman et alli (2018) and other empirical non-parametric models. By conducting an extensive walk-forward forecasting exercise we conclude that the new model outperforms both the empirical non-parametric predictors and the score-driven model for the forecasting the conditional bivariate distribution. We also conclude that the Score Driven outperforms all the empirical non-parametric models considered.