Copula based models for serial dependence

Abstract

This paper is concerned with the statistical modeling of the dependence structure in the ¯rst and second moments of a univariate ¯nancial time series using the concept of copulas. The appealing feature of the method is that it captures not just the linear form of dependence (a job usually accomplished by ARIMA linear models), but also the non-linear ones, including tail dependence, the dependence occuring only among extreme values. In addition we investigate the changes in the mean modeling after whitening the data through the application of GARCH type ¯lters. Sixty two U.S. stocks are selected to illustrate the methodologies. The copula based results corroborate empirical evidences on the existence of linear and non-linear dependence at the mean and at the volatility levels, and contributes to practice by providing yet a simple but powerful method for capturing the dynamics in a time series. Applications may follow and include VaR calculation, simulations based derivatives pricing, and asset allocation decisions. We recall that the literature is still inconclusive as to the most appropriate Value-at-Risk computing approach, which seems to be a data dependent decision.