Statistical modelling of temporal dependence in financial data via a copula function

In financial analysis it is useful to study the dependence betweentwo or more time series as well as the temporal dependence in aunivariate time series. This paper is concerned with the statisticalmodelling of the dependence structure in a univariate financial timeseries using the concept of copula. We treat the series of financialreturns as a first order Markov process. The Archimedeantwo-parameter BB7 copula is adopted to describe the underlyingdependence structure between two consecutive returns, while thelog-Dagum distribution is employed to model the margins marked byskewness and kurtosis. A simulation study is carried out to evaluatethe performance of the maximum likelihood estimates. Furthermore, we apply the model to the daily returns of four stocks and, finally, we illustrate how its fitting to data can be improved when the dependence between consecutive returns is described through a copula function.