Contents -- Preface -- 1. Introduction: Dependence Modeling D. Kurowicka -- 1.1 Introduction -- 1.2 Investment Example -- 1.3 Vines -- 1.3.1 Graphical representation -- 1.3.2 Vine density -- 1.3.3 Estimation -- 1.3.4 Properties and applications -- 1.4 Outline -- 1.5 Glossary and Notation -- References -- 2. Multivariate Copulae M. Fischer -- 2.1 Copulae -- 2.2 Elliptical Copulae and Generalizations -- 2.2.1 Elliptical copulae -- 2.2.2 Generalized t-copulae -- 2.3 Archimedean Copulae and Generalizations -- 2.3.1 Classical Archimedean copulae -- 2.3.2 Non-exchangeable Archimedean copulae -- 2.3.3 Generalized multiplicative Archimedean copulae -- 2.3.4 Koehler-Symanowski copulae -- 2.4 Combinations of Arbitrary Copulae into a New One -- 2.5 Summary -- References -- 3. Vines Arise R. M. Cooke, H. Joe and K. Aas -- 3.1 Introduction -- 3.2 Regular Vines -- 3.3 Vine Types -- 3.3.1 Vine copula or pair-copula construction -- 3.3.2 Partial correlation vine -- 3.3.2.1 Partial correlation -- 3.3.2.2 Partial correlation vine -- 3.3.2.3 Applications -- 3.4 Historical Origins -- 3.5 Compatibility of Marginal Distributions -- 3.6 Sampling -- 3.6.1 Sampling a D-vine -- 3.6.2 Sampling an arbitrary regular vine -- 3.6.3 Density approach sampling -- 3.7 Parametric Inference for a Specific Pair-Copula Construction -- 3.7.1 Inference for a C-vine -- 3.7.2 Inference for a D-vine -- 3.8 Model Inference -- 3.8.1 Sequential selection -- 3.8.2 Information-based model inference -- 3.8.2.1 Definitions and theorems -- 3.9 Applications -- 3.9.1 Multivariate data analysis -- 3.9.2 Non-parametric Bayesian belief nets -- References -- 4. Sampling Count Variables with Specified Pearson Correlation: A Comparison between a Naive and a C-Vine Sampling Approach V. Erhardt and C. Czado -- 4.1 Introduction -- 4.2 Copulae and Multivariate Distributions.

4.3 Naive Sampling with Illustration to GP Count Data -- 4.4 Simulation Study -- 4.5 Summary and Discussion -- Acknowledgments -- References -- 5. Micro Correlations and Tail Dependence R. M. Cooke, C. Kousky and H. Joe -- 5.1 Introduction -- 5.2 Micro Correlations -- 5.3 Tail Dependence and Aggregation -- 5.3.1 Latent variable models for tail dependence -- 5.3.2 Sum of damages over extreme events -- 5.3.3 L1-symmetric measures -- 5.3.4 Tail dependence for sums of L1 measures -- 5.3.5 Lower tail dependence -- 5.4 Discussion -- Appendices -- References -- 6. The Copula Information Criterion and Its Implications for the Maximum Pseudo-Likelihood Estimator S. Grønneberg -- 6.1 Introduction -- 6.2 The Developments Leading to the CIC -- 6.2.1 The fully parametric MLE -- 6.2.2 Kullback-Leibler divergence and model selection -- 6.2.3 The MPLE, the empirical copula and invariance considerations -- 6.2.4 What about semiparametric efficiency? -- 6.2.5 Large-sample theory for the MPLE -- 6.3 Model Selection with the MPLE -- 6.3.1 Non-existence of bias-correction terms and implications for the MPLE -- 6.3.2 Philosophical implications of the CIC -- 6.4 Illustrations -- 6.5 Concluding Remarks -- Acknowledgments -- References -- 7. Dependence Comparisons of Vine Copulae with Four or More Variables H. Joe -- 7.1 Introduction -- 7.2 Equivalence Classes of Regular Vines -- 7.3 Simulation from Vine Copulae -- 7.4 Comparing Dependence of Vine Copulae -- 7.5 Gaussian Vines and Generalized Toeplitz Matrices -- 7.6 More Comparisons of Dependence for Different Vines -- 7.7 Discussion and Further Research -- Acknowledgments -- References -- 8. Tail Dependence in Vine Copulae H. Joe -- 8.1 Introduction -- 8.2 Tail Dependence in Different Multivariate Copula Families -- 8.3 Tail Dependence Parameters and Functions -- 8.3.1 Bivariate tail dependence.

8.3.2 Multivariate tail dependence functions -- 8.3.3 Conditional tail dependence functions -- 8.4 Main Theorem on Tail Dependence for Vine Copulae -- 8.5 Reflection Asymmetry of Vine Copulae -- 8.6 Choice of Tail Asymmetric Bivariate Linking Copulae -- 8.7 Discussion -- Acknowledgments -- Appendix -- References -- 9. Counting Vines O. Morales-Napoles -- 9.1 Introduction -- 9.2 Basic Definitions -- 9.3 Regular Vines and Prufer Codes -- 9.4 Regular Vines and Line Graphs -- 9.5 Regular Vines and Regular Vine Arrays -- 9.6 Classifying Regular Vines -- 9.7 Conclusions and Final Comments -- Appendix -- References -- 10. Regular Vines: Generation Algorithm and Number of Equivalence Classes H. Joe, R. M. Cooke and D. Kurowicka -- 10.1 Introduction -- 10.2 Naming Convention for Vines -- 10.3 Number of Equivalence Classes -- 10.4 Examples -- 10.5 Discussion -- Reference -- 11. Optimal Truncation of Vines D. Kurowicka -- 11.1 Introduction -- 11.2 Vines -- 11.3 Vine Distributions -- 11.3.1 Markov trees -- 11.3.2 Vines in trees -- 11.4 Optimal Truncation -- 11.4.1 Generating regular vines -- 11.4.2 Best vine -- 11.5 Optimal Truncation: Results -- 11.5.1 Example -- 11.5.2 Comparison -- 11.6 Conclusions -- References -- 12. Bayesian Inference for D-Vines: Estimation and Model Selection C. Czado and A. Min -- 12.1 Introduction -- 12.2 D-Vine -- 12.3 D-Vine PCC Based on t-Copulae -- 12.4 Bayesian Inference for D-Vine PCC Based on t-Copulae -- 12.5 Application: Australian Electricity Loads -- 12.6 Bayesian Model Selection for Australian Electricity Loads -- 12.7 Summary and Discussion -- Acknowledgments -- References -- 13. Analysis of Australian Electricity Loads Using Joint Bayesian Inference of D-Vines with Autoregressive Margins C. Czado, F. Gärtner and A. Min -- 13.1 Introduction.

13.2 Multivariate Time Series with D-Vine Dependency and Marginal Autoregressive Structure -- 13.3 Bayesian Analysis of Multivariate Time Series with D-Vine Dependency and Marginal Autoregressive Structure -- 13.4 Modeling Australian Electricity Loads -- 13.5 Bayesian Model Selection -- 13.6 Summary and Discussion -- Acknowledgments -- References -- 14. Non-Parametric Bayesian Belief Nets versus Vines A. Hanea -- 14.1 Introduction or: How to Represent Information Burdened by Uncertainty -- 14.2 Non-Parametric Bayesian Belief Nets: Sampling and Conditionalizing -- 14.2.1 Sampling an NPBBN -- 14.2.2 Conditionalizing an NPBBN -- 14.3 Data Mining with NPBBNs -- 14.4 Applications of NPBBNs -- 14.5 Conclusions -- References -- 15. Modeling Dependence between Financial Returns Using Pair-Copula Constructions K. Aas and D. Berg -- 15.1 Introduction -- 15.2 Constructions of Higher-Dimensional Dependence -- 15.2.1 Student copula -- 15.2.2 Partially nested Archimedean construction (PNAC) -- 15.2.3 Pair-copula construction (PCC) -- 15.3 Parameter Estimation -- 15.3.1 Student copula -- 15.3.2 PNAC -- 15.3.3 PCC -- 15.4 Portfolio 1 -- 15.4.1 Data set -- 15.4.2 Results -- 15.4.2.1 PNAC -- 15.4.2.2 PCC -- 15.4.3 Validation -- 15.5 Portfolio 2 -- 15.5.1 Data set -- 15.5.2 Results -- 15.5.2.1 PCC -- 15.5.2.2 Four-dimensional Student copula -- 15.5.3 Tail dependence -- 15.5.4 Pair-copula decomposition with copulae from di.erent families -- 15.6 Summary and Conclusions -- Acknowledgments -- References -- 16. Dynamic D-Vine Model A. Heinen and A. Valdesogo -- 16.1 Introduction -- 16.2 The Model -- 16.2.1 Copulae -- 16.2.1.1 Copula-based dependence measures -- 16.2.1.2 Asymmetric dependence, exceedance correlation and tail dependence -- 16.2.2 D-vine copula -- 16.2.3 Dynamic D-vine model -- 16.3 Components of the Model -- 16.3.1 Marginal model -- 16.3.2 Bivariate copulae.

16.3.2.1 Gaussian copula -- 16.3.2.2 Student t-copula -- 16.3.2.3 Frank copula -- 16.3.2.4 Gumbel and rotated Gumbel copula -- 16.3.2.5 Clayton copula -- 16.4 Empirical Results -- 16.4.1 Data -- 16.4.2 Marginal models -- 16.4.3 Copula structure -- 16.5 Conclusion -- References -- 17. Summary and Future Directions D. Kurowicka -- 17.1 Summary -- 17.2 Future Research Directions -- Index.