Copulas: Quest and Conquest

May 23, 9:00 am – 12:00 pm, 1:30 – 4:00 pm
 

By Christian Genest, Université Laval and Johanna Nešlehová, McGill University
 

Copulas are multivariate distributions whose margins are uniform on the interval (0, 1). They provide a handy tool for modeling the dependence between variables whose distributions are heterogeneous or involve covariates. Due to their flexibility, copula models are quickly gaining popularity in hydrology, finance and insurance. This workshop aims to provide an introduction to statistical inference for copula models and its implementation in the R project for statistical computing. The notion of copula and its role in representing dependence will first be reviewed. A few classical copula models will then be described, along with their properties. Next, it will be shown how estimation and goodness-of-fit testing can be performed using rank-based methods. Diagnostic tools for the detection of dependence and copula selection will also be presented. Special attention will be devoted to extreme-value dependence. The continuous case will be considered in detail; adjustments required for handling discrete variables will be mentioned. Data from hydrology, actuarial science and finance will be used for illustration purposes.