Although it is stand-alone, this tutorial can be seen as the last module of the winter course. It will start by an overview of copula theory and related statistical inference, and will then address more advanced topics such as the handling of non-stationarity, serial dependence, filtering and ties. All the presented concepts will be illustrated by reproducible R examples involving either synthetic or real data.

Copula models have showed several advantages in describing the behavior of a multivariate stochastic system (e.g., a risk portfolio) because of their flexibility in describing various dependence aspects. In particular, from a risk management perspective, special care should be devoted to the description of the dependence in the tails of the joint distribution function.
Here we focus on some selected investigations about tail dependence (as described by means of copulas) and its possible applications. Our aim is to provide some theoretical, computational and graphical tools that may help the decision maker in the correct identification of linkages among different random variables, especially in a risky scenario.