Copula Modelling to Analyse Financial Data

Abstract

Copula modelling is a popular tool in analysing the dependencies between variables. Copula modelling allows the investigation of tail dependencies, which is of particular interest in risk and survival applications. Copula modelling is also of specific interest to economic and financial modelling as it can help in the prediction of financial contagion and periods of “boom” or “bust”. Bivariate copula modelling has a rich variety of copulas that may be chosen to represent the modelled dataset dependencies and possible extreme events that may lie within the dataset tails. Financial copula modelling tends to diverge as this richness of copula types within the literature may not be well realised with the two different types of modelling, one being non-time-series and the other being time-series, being undertaken differently. This paper investigates standard copula modelling and financial copula modelling and shows why the modelling strategies in using time-series and non-time-series copula modelling is undertaken using different methods. This difference, apart from the issues surrounding the time-series component, is mostly due to standard copula modelling having the ability to use empirical CDFs for the probability integral transformation. Financial time-series copula modelling uses pseudo-CDFs due to the standardized time-series residuals being centred around zero. The standardized residuals inhibit the estimation of the possible distributions required for constructing the copula model in the usual manner.