Joint modelling of the body and tail of bivariate data

TL;DR

This paper introduces a novel dependence model that combines two copulas with a dynamic transition to accurately capture both the bulk and tail dependence in bivariate data, demonstrated through environmental data analysis.

Contribution

A new blended copula model with a dynamic weighting function that effectively captures complex dependence structures across the entire data range.

Findings

The model outperforms single copula fits in flexibility and accuracy.

It successfully captures diverse dependence structures in simulated data.

Applied to UK temperature and ozone data, it provides a better fit than traditional models.

Abstract

In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been extensively studied before. However, when more than one variable is of concern, models that aim specifically at capturing both regions correctly are scarce in the literature. A dependence model that blends two copulas with different characteristics over the whole range of the data support is proposed. One copula is tailored to the bulk and the other to the tail, with a dynamic weighting function employed to transition smoothly between them. Tail dependence properties are investigated numerically and simulation is used to confirm that the blended model is sufficiently flexible to capture a wide variety of structures. The model is applied to study the dependence between temperature and ozone concentration at two sites in the UK and compared with a single copula fit. The proposed model provides a better, more flexible, fit to the data, and is also capable of capturing complex dependence structures.