Dynamic discrete copula models for high‐frequency stock price changes

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.