# Introduction to the modelling of continuous multivariate distributions using copulas

#### Lecturers

Professor Ivan Kojadinovic, University of Pau, France

#### Synopsis

Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modelling dependence among random variables in probabilistic and statistical models arising in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, meteorology, to name a few. The aim of the course is to introduce the main theoretical results about copulas and to show how statistical modelling of multivariate continuous distributions using copulas can be carried out in the R statistical environment.

#### Course Overview

• Part 1: Basic introduction to copulas and their main properties, along with the most important theoretical results.
• Part 2: The most widely used copula classes, their corresponding sampling procedures, along with selected copula transformations that are important for practical purposes.
• Part 3: Estimation of copulas from a parametric, semi-parametric and non-parametric perspective.
• Part 4: Graphical diagnostics, statistical tests and model selection.
• Part 5: Dealing with non-stationarity, serial dependence and ties in copula inference.

All the presented concepts will be illustrated by stand-alone and reproducible R examples involving either synthetic or real data. Advanced topics such as dynamic copula models are not covered. This course is based on the book https://www.springer.com/fr/book/9783319896342.

This is intended to be a foundational course for students.

#### Prerequisites

• Knowledge of basic univariate and multivariate probability and statistics (distribution and density functions, estimation principles, basic laws, …).
• Basic knowledge of the R programming language.

Participants will be expected to have their own laptop with the latest versions of R and the R packages copula, mvtnorm, nor1mix, qrmtools, qrng, MASS, bbmle, latticeExtra, xts, npcp, rugarch, copulaData and lattice installed.

A link with some material will be provided to the students.

#### Assessment

• 2 tests – 25% each (50% total)
• Final exam – 50%

#### Attendance requirements

• For those completing the subject for their own knowledge/interest, evidence of attendance at all lectures is required in order to receive a certificate of attendance.