Statistical Modeling of Temporal Dependence in Financial Data via a Copula Function

Abstract

In financial analysis it is useful to study the dependence between two or more time series as well as the temporal dependence in a univariate time series. This article is concerned with the statistical modeling of the dependence structure in a univariate financial time series using the concept of copula. We treat the series of financial returns as a first order Markov process. The Archimedean two-parameter BB7 copula is adopted to describe the underlying dependence structure between two consecutive returns, while the log-Dagum distribution is employed to model the margins marked by skewness and kurtosis. A simulation study is carried out to evaluate the 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.

Keywords:

• Archimedean copula function
• Log-Dagum distribution
• Markov process
• Returns
• Tail dependence

Mathematics Subject Classification:

• 62F10
• 62M05
• 62H20

Acknowledgments

The work has been supported by Murst ex-60% funds, University of Calabria. The authors wish to thank Professor Ivar Massabó and two anonymous referees for their careful reading and constructive suggestions which led to improvements over an earlier version of the article.