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The authors introduce a multivariate GARCH-Copula model to describe joint dynamics of overnight and daytime returns for multiple assets. The conditional mean and variance of individual overnight and daytime returns depend on their previous realizations through a variant of GARCH specification, and two Student's t copulas describe joint distributions of both returns respectively. They employ both constant and time-varying correlation matrices for the t copulas and with the time-varying case the dependence structure of both returns depends on their previous dependence structures through a DCC specification. They estimate the model by a two-step procedure, where marginal distributions are estimated in the first step and copulas in the second.
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