Modulbeschreibung MA5408

# Modulbeschreibung

## MA5408: Statistische Analyse von Kopulas

### Fakultät für Mathematik

Modulniveau:
Master
Sprache:
Englisch
Semesterdauer:
Einsemestrig
Häufigkeit:
Unregelmäßig
Credits*:
5
Gesamt-
stunden:

150
Eigenstudiums-
stunden:

105
Präsenz-
stunden:

45
* Die Zahl der Credits kann in Einzelfällen studiengangsspezifisch variieren. Es gilt der im Transcript of Records oder Leistungsnachweis ausgewiesene Wert.
Beschreibung der Studien-/Prüfungsleistungen:
In this 60-min written exam the students prove that they are able to work with and differentiate between (tail) dependence measures and multivariate distributions. They show that they can select from graphical displays appropriate bivariate copula families. In the area of multivariate copula theory they are able to construct the likelihood of vine copulas from the vine, family and parameter matrices. This also includes the construction of tree plots, code to fit these models in VineCopula and derive conditional distributions associated with a vine distributions. Further they can describe how simulation, estimation and model selection algorithms work and are able to give data specific interpretations of results.
Wiederholungsmöglichkeit:
Im Folgesemester: keine Angabe
Am Semesterende: Ja
(Empfohlene) Voraussetzungen:
MA2409 Probability Theory, MA2402 Basics Statistics,
R Knowledge
Time Series, Quantitative Risk Measures
Angestrebte Lernergebnisse:
At the end of the module, the student is able to understand, analyse and apply vine copula based models.
For this the student knows the most prominent families of bivariate copulas and their properties, which are the building blocks of vine copulas. Further she or he knows parameter and model selection methods tailored to vine distributions and is able to select appropriate vine copula based models to a given multivariate data set using the
VineCopula R package.
Inhalt:
Introduction to multivariate distributions, dependence measures and copulas. Bivariate copula classes and their visualization (elliptical, Archemedian, extreme value copulas). Fundamentals of Pair copula constructions yielding canonical (C), drawable (D) and regular (R) vines.
Simulation from C,D and R vines. Parameter estimation in vines and applications using the CDVine() and VineCopula() R packages. Inference techniques for vine copula based models (Inference for margins (IFM) and maximum pseudo likelihood (MPL)). Comparison and copula goodness-of-fit-tests. Model selection of regular vines. Bayesian estimation and model selection. Special vine models: Vine sector models, time varying vines, Markov switching vines, factor vines. Discrete and discrete-continuous vines.
Lehr- und Lernmethode:
lecture, theoretical and data exercises for self study
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.
Medienformen:
Blackboard, exercise sheets, data analysis, reserved books in library,
moodle course
Literatur:
Aas, K., Czado, C., Frigessi, A., Bakken, H.: Pair-copula constructions of multiple dependence. Insurance, Mathematics and Economics 44, 182198 (2009).
Kurowicka, D., Joe, H.: Dependence Modeling - Handbook on Vine Copulae. World Scientific Publishing Co., Singapore (2011).
Vine Copula Resource Page: vine-copula.org
Modulverantwortliche(r):