Koopman, S.J., Lit, R., Lucas, A. and Opschoor, A. (2018). Dynamic discrete copula models for high-frequency stock price changes Journal of Applied Econometrics, 33(7):966--985.

We develop a dynamic model for the intraday dependence between discrete stock price changes. The conditional copula mass function for the integer tick-size price changes has time-varying parameters that are driven by the score of the predictive likelihood function. The marginal distributions are Skellam and also have score-driven time-varying parameters. We show that the integration steps in the copula mass function for large dimensions can be accurately approximated via numerical integration. The resulting computational gains lead to a methodology that can treat high-dimensional applications. Its accuracy is shown by an extensive simulation study. In our empirical application of 10 US bank stocks, we reveal strong evidence of time-varying intraday dependence patterns: Dependence starts at a low level but generally rises during the day. Based on one-step-ahead out-of-sample density forecasting, we find that our new model outperforms benchmarks for intraday dependence such as the cubic spline model, the fixed correlation model, or the rolling average realized correlation.