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.

Assessment of Hydrological and Meteorological Composite Drought Characteristics Based on Baseflow and Precipitation

“…Among them, the Frank copula function has a simple structure. It can be used to describe the symmetric correlation structure, which applies to both positive and negative correlations and has no limitation on the degree of correlation, and the variation in the upper and lower tails of the correlations is not apparent [45]. Many drought studies have used the Frank copula function [46][47][48].…”

Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics

“…Copula regression is a methodology that allows nonlinear dependence to be modeled and is a realistic way of describing multivariate distributions, see Dewick and Liu (2022) and Parsa and Klugman (2011). However, if the true copula structure has been misspecified, copula regression does not yield reliable estimates of the regression function, see Dette et al (2014).…”

“…Moreover, in general, a copula can be difficult to estimate due to the generality of copulas, see Schmidt (2007). For more details about Copula and its appli-cations, see, e.g., Dewick and Liu (2022). Noting that copula modeling carries a risk of misspecification, the definition of copula regression is given in Definition 6.…”

“…To further aid in identifying a suitable regression modeling methodology (both elliptical and skew-elliptical), copula modeling can be utilized. Copula modeling allows for the identification of the underlying distribution, such as normal, Student's t, Gumbel, BB1, and others, as described in Dewick and Liu (2022).…”

Generation of realistic virtual adult populations using a model-based copula approach

“…Copula models are statistical models which capture the dependence structure between random variables independently from the description of the marginals [7]. A rich variety of copula models is available to be selected to estimate diverse dependent patterns in data [8]. Using a transformation of any marginal distribution to a uniform distribution, the dependence structure can be separated from the marginal structure.…”