Due to their flexibility, copula models are quickly gaining popularity in applied research. Copulas are
descriptions of multivariate distributions whose margins are uniform. This course gives an introduction to
the class of vine copulas and their statistical inference. Vine copula models have become very popular in
the last years for many applications in diverse fields such as finance, insurance, hydrology, marketing,
engineering, chemistry, aviation, climatology and health. This course provides an introductio

On completion of the course, the students will be able to:

• Demonstrate understanding and knowledge regarding the theoretical background of vine copula

models and their statistical inference.

• Demonstrate understanding regarding the difference between regular, drawable and canonical

vines.

• Interpret and analyze results derived from vine copula models.
• Perform statistical tests in the framework of vine copulas to select the appropriate model.
• Estimating vine copula dependence models using multivariate data.
• Apply the statistical software R to conduct copula-based modeling and perform simulations based on the estimated model.

• Critically evaluate the appropriateness of vine copulas in multivariate data analysis

The course starts with a background chapter on multivariate and conditional distributions
and copulas. This includes the parametric classes of elliptical, Archimedean and extreme value copulas. Their
parameter estimation and graphical tools for the identification of sensible bivariate copula models to
data are presented. The decomposition and construction principle of drawable (D-), canonical (C-) and
regular (R-) vines is developed and discussed. The course concludes with recent extensions of vines
including advances in estimation, model selection, for special data structures and reviews major applications
in finance, life and earth sciences, insurance and engineering. It also provides an overview of the available
software, in particular R, to select, estimate and visualize vinebased models.

The course is designed as a series of lectures, seminars and computer labs.

Undervisningen bedrivs på engelska.

Admitted to a doctoral program in statistics or a related subject of a recognized business school or
university.

Kursen bedöms med betygen Underkänd eller Godkänd.

This course is examined using a course paper where a copula-based modeling of multivariate data should
be performed. This paper deals with ILOs 1,2,3,4,5,6,7
The grades given are pass or fail.

A course evaluation will be conducted at the end of the course.

Claudia C, Analyzing Dependent Data with Vine Copulas: A practical Guide with R, 2019, Springer, New
York.
Joe, H. (2014). Dependence modeling with copulas. CRC Press
Additional readings, to be assigned during the lectures.