Participants will be expected to have their own laptop with the latest versions of R and the R packages copula, lcopula, npcp, qrmtools, rugarch, timeSeries and xts installed.
PhD students and Early Career Investigators (who have obtained their PhD degree in 2010 or after) can apply for a limited number of grants of 500 Euro for accommodation and traveling and will have their fees for the course waived.
Organized by the CRoNos COST Action IC1408 represented by
Erricos J. Kontoghiorghes and Ana Colubi.
Sponsored by COST
Wednesday, 13 December 2017
Thursday, 14 December 2017
Friday, 15 December 2017
Summary: Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling 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 this short course is to introduce the main theoretical results about copulas and to show how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment.
Sessions 1.1 and 1.2: Basic introduction to copulas and their main properties, along with the most important theoretical results.
Session 1.3: The most widely used copula classes, their corresponding sampling procedures, along with selected copula transformations that are important for practical purposes.
Sessions 1.4 and 1.5: Estimation of copulas from a parametric, semi-parametric and non-parametric perspective.
Sessions 1.6 and 1.7: Graphical diagnostics, statistical tests and model selection.
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 or vine copulas are not covered.
Summary: 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.
Summary: 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.