Long Range Dependence in Copula Models

Modeling short and long time dependence in univariate time series may be successfully accomplished through existing time series processes. In the multivariate setting just a few complex models exist to take care of the di®erent marginal dynamics as well as of the dynamic covariance matrix. The copula approach factors the joint distribution into the marginals and a dependence function, its copula. This allows for tailored marginal dynamic modeling of each margin, considering all characteristics of each marginal distribution, including skewness, kurtosis and any type of short and long memory serial dependence, plus a search for the best ̄t for the dependence structure which is entirely determined by the copula. Assuming a conditional copula model, depending on past observations, enhances the ̄t. Attempts to model serial correlation in copula environment are only a few, moreover just short memory is considered. However, the dependence structure linking the series may also possess long memory. For example, the dependence structure associated with the standardized residuals from a FIGARCH ̄t on log-returns may still present long memory. Moreover, long memory could be present only in the dependence structure and not in the margins. In this paper we propose a proxy for detecting long memory in the copula function. We show how to simulate from a copula possessing long memory, we discuss inference methods, and provide an application using real data. JEL subject classi ̄cations: C22 C51 G10