Dynamic discrete copula models for high-frequency stock price changes

Siem Jan Koopman*, Rutger Lit, André Lucas, Anne Opschoor

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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.

Original languageEnglish
Article number33
Pages (from-to)966-985
Number of pages20
JournalJournal of Applied Econometrics
Issue number7
Early online date9 Aug 2018
Publication statusPublished - Nov 2018


Lit and Lucas acknowledge the financial support of the Dutch National Science Foundation (NWO, grant VICI453-09-005). Koopman acknowledges the support from CREATES, the Center for Research in Econometric Analysis of Time Series (DNRF78) at Aarhus University, Denmark, funded by the Danish National Research Foundation.

FundersFunder number
Center for Research in Econometric Analysis of Time SeriesDNRF78
Aarhus Universitet
Danmarks Grundforskningsfond
Nederlandse Organisatie voor Wetenschappelijk OnderzoekVICI453-09-005


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