Julius Schnieders

Analyzing and Modeling Multivariate Association

Statistical Measures and Pair-Copula Constructions

• Broschiertes Buch

Produktbeschreibung

Many applications in quantitative finance, such as the estimation of the Value-at-Risk of a portfolio, require the modeling of dependencies of a large number of random variables. The most popular approach is Pearson¿s correlation coefficient, which is based on the covariance, i. e. the mixed second moments of the corresponding random variables. However, the correlation coefficient only captures linear dependencies and solely in case of a few distributions, such as the multivariate normal distribution, completely determines the dependence structure. Empirical data, unfortunately, is often non-normal and exhibits asymmetric dependence patterns. The multivariate normal distribution, for example, often underestimates the probability of simultaneous extremes, which can lead to incorrect estimates of the risk of a given portfolio. Hence, for many empirical applications, the normal distribution is not suitable. As an alternative concept of dependence modeling, the theory of copulas has drawn a lot of attention in the past decades. Based on this theory, the author introduces a new class of measures of association between random vectors that are invariant with respect to the marginal distribution functions of the considered random vectors and can distinguish between positive and negative association. The second part of the thesis focuses on the modeling of high dimensional dependencies with Pair-copula constructions. To this end, a data-driven sequential estimation method for these models is developed. Empirical applications of these models in Value-at-Risk forecasting and the spatial modeling of meteorological data are given.

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Produktdetails

• Quantitative Ökonomie, Bd. 176
• Verlag: Eul, Josef, Verlag GmbH / Josef Eul Verlag GmbH
• Seitenzahl: 228
• Erscheinungstermin: 5. März 2013
• Englisch
• Abmessung: 210mm x 148mm x 15mm
• Gewicht: 337g
• ISBN-13: 9783844102291
• ISBN-10: 3844102299
• Artikelnr.: 37389536

Autorenporträt

Julius Schnieders, born in 1983, studied Mathematics with a focus on Statistics in Münster and Madrid. He finished his studies in 2008 and became a member of the Graduate School of Risk Management at the University of Cologne. In 2012, he completed his doctoral studies in Statistics at the Chair of Economic and Social Statistics of Prof. Dr. Friedrich Schmid. He has written articles on dependence modeling, and has given presentations on this subject at several international conferences.

Inhaltsangabe

1. Introduction 2. Copulas and Dependence Concepts 2.1. Theory of Copulas
2.2. Parametric Copula Families 2.3. Survival and rotated copulas 2.4. The
empirical copula 2.5. Measures of Association 3. Association of Random
Vectors 3.1. Notation and definitions 3.2. Established measures of
association 3.3. Copula based measures of association 3.4. Statistical
estimation of the measures 3.5. Empirical example 3.6. Influence of
outliers 3.7. Conclusion 4. Pair-Copula Constructions 4.1. Pair-Copula
Constructions 4.2. Conditional distribution functions 4.3. Vines 4.4.
Simplified PCCs 4.5. Estimation of Pair-Copula Constructions 4.6.
Simulation Techniques 4.7. Conclusion 5. Model Selection for Pair-Copula
Constructions 5.1. Model Selection for bivariate copulas 5.2.
Goodness-of-Fit 5.3. Model selection for Vine Structures 5.4. Simulation
Study 5.5. Application to Empirical Datasets 5.6. Conclusion 6. Application
of Pair-Copula Constructions 6.1. Dynamic PCC Models: An Application with
Value-at-Risk Forecasting 6.2. Spatial dependence in wind and optimal wind
power allocation