This page provides an extensive overview of research on vine copula models.
Please note that all manuscript files are for private use only and may not be distributed without permission of the respective copyright owners.

• Czado, C. (2011)
  The World of Vines
  Presentation at the 4th Workshop on Vine Copula Distributions and Applications, TU München
  [.pdf]
• Krämer, N., Schepsmeier, U. (2011)
  Introduction to Vine Copulas
  Tutorial at the NIPS'11 Workshop on Copulas in Machine Learning, Sierra Nevada
  [.pdf]
• Cooke, R. M. (2007)
  Vines in Overview
  Invited Paper: Third Brazilian Conference on Statistical Modeling in Insurance and Finance, Maresias 
  [.pdf]
 

Videos of the Workshop "Non-Gaussian Multivariate Statistical Models and their Applications" (2013)
Banff International Research Station for Mathematical Innovation and Discovery, Canada

• Kjersti Aas, Norwegian Computing Center, and Claudia Czado, Technische Universität Muenchen (May 20, 2013)
  Pair-copula constructions – even more flexible than copulas
  [Watch video] [Download video (155 MB)]
• Dorota Kurowicka, Nanyang Technological University (May 23, 2013)
  Joint density of correlations in correlation matrix with chordal sparsity patterns
  [Watch video] [Download video (93 MB)]
• Eike Brechmann, Technische Universität Muenchen (May 23, 2013)
  Statistical Inference of Vine Copulas using the R-Package VineCopula
  [Watch video] [Download video (101 MB)]
  
  

• Czado, C., E.C. Brechmann and L. Gruber (2013)
  Selection of Vine Copulas
  To appear in: P. Jaworski, F. Durante and W. K. Härdle (Eds.),Copulae in Mathematical and Quantitative Finance, Springer.
  [link]
• Stoeber, J. and C. Czado (2012),
  Sampling Pair Copula Constructions with Applications to Mathematical Finance.
  In J.-F. Mai and M. Scherer (2012), Simulating Copulas: Stochastic Models, Sampling Algorithms, and Applications.
  Singapore: World Scientific Publishing Co.
  [link]
• Kurowicka, D. and H. Joe (2011)
  Dependence Modeling - Handbook on Vine Copulae.
  Singapore: World Scientific Publishing Co.
  [link]
• Czado, C. (2010)
  Pair-copula constructions of multivariate copulas
  In P. Jaworski, F. Durante, W. Härdle, and T. Rychlik (Eds.), Copula Theory and Its Applications. Berlin: Springer. 
  [link | preprint]
• Kurowicka, D. and R. Cooke (2006)
  Uncertainty analysis with high dimensional dependence modelling.
  Chichester: Wiley.
  [link]
  
  

• Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009).
  Pair-copula constructions of multiple dependence
  Insurance: Mathematics and Economics 44 (2), 182-198. 
  [link | preprint]
• Berg, D. and K. Aas (2009). 
  Models for construction of higher-dimensional dependence: A comparison study
  European Journal of Finance 15, 639-659. 
  [link|.pdf]
• Bedford, T. and R. M. Cooke (2002). 
  Vines - a new graphical model for dependent random variables.
  Annals of Statistics 30, 1031-1068.
  [link]
• Bedford, T. and R. M. Cooke (2001).
  Probability density decomposition for conditionally dependent random variables modeled by vines
  Annals of Mathematics and Artificial intelligence 32, 245-268. 
  [link]
• Joe, H. (1996).
  Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters.
  In L. Rüschendorf and B. Schweizer and M. D. Taylor (Ed.), Distributions with Fixed Marginals and Related Topics.
  [link]
  
  

• Workshop: Copulae in Mathematical and Quantitative Finance
  July 10-11, 2012, Kraków - Przegorzaly
  [link]
  -> Short course on July 9, 2012: "Vine copulae; Simulation; Estimation methods; Model selection; Truncation; Vine sector models".
  [link]
• 4th Workshop on Vine Copula Distributions and Applications
  May 11-12, 2011 Technische Universität München
  [link]
  
  

• Kurowicka, D. and Cooke, R. M. (2007)
  Sampling algorithms for generating joint uniform distributions using the vine-copula method
  Computational Statistics and Data Analysis 51(6), 2889-2906.
  [pdf]
• Kurowicka, D. and Cooke, R. M. (2006)
  Completion problem with partial correlation vines
  Linear Algebra and its Applications 418, 188-200.
  [pdf]
• Kurowicka, D. and Cooke, R. M. (2003)
  A parameterization of positive definite matrices in terms of partial correlation vines
  Linear Algebra and its Applications 372, 225-251.
  [pdf]
• Cooke, R. M. (1997)
  Markov and entropy properties of tree- and vine-dependent variables
  Proceedings of the ASA Section on Bayesian Statistical Science.
  [pdf]

• Stoeber, J.,  H. Joe and C. Czado (2013),
  Simplified Pair Copula Constructions - Limitations and Extensions
  Journal of Multivariate Analysis, 119, 101-118
  [pdf]
• Lopez-Paz D, Hernandez-Lobato JM and Ghahramani Z (2013)
  Gaussian Process Vine Copulas for Multivariate Dependence
  In: JMLR W&CP 28(2): Proceedings of The 30th International Conference on Machine Learning, (Ed) S Dasgupta and D McAllester, 30th International Conference on Machine Learning (ICML 2013), JMLR, 10-18.
  [pdf]
• Haff, I. H., K. Aas, and A. Frigessi (2010).
  On the simplified pair-copula construction – simply useful or too simplistic?
  Journal of Multivariate Analysis 101(5), 1296–1310.
  [pdf]

• Schepsmeier, U. (2013),
  A goodness-of-fit test for regular vine copula models.
  submitted for publication
  [pdf]
• Dißmann, J., Brechmann, E.C., Czado, C., and Kurowicka, D.  (2013)
  Selecting and estimating regular vine copulae and application to financial returns 
  Computational Statistics and Data Analysis, 59, 52-69
  [pdf]
• Brechmann, E.C., Czado, C. and Aas, K. (2012) 
  Truncated regular vines in high dimensions with applications to financial data
  Canadian Journal of Statistics, 40 (1), 68-85
  [pdf]
• Czado, C., S. Jeske and M. Hofmann (2012)
  Selection strategies for regular vine copulae
  Submitted for publication
  [link]
• Czado, C. and Min, A. (2011),
  Bayesian Inference for D-vines: Estimation and Model Selection
  (Handbook on Vines, Editors: Dorota Kurowicka and Harry Joe, World Scientific)
• Min, A. and C. Czado (2010).
  Bayesian model selection for multivariate copulas using pair-copula constructions.
  Journal of Financial Econometrics 8 (4), 511–546.
  [pdf]
• Min, A. and C. Czado (2010). 
  Bayesian model selection for D-vine pair-copula constructions. 
  Canadian Journal of Statistics 39 (2), 239–258.
  [pdf]
• Smith, M., A. Min, C. Almeida, and C. Czado (2010).
  Modeling longitudinal data using a pair-copula construction decomposition of serial dependence.
  Journal of the American Statistical Association 105, 1467–1479.
  [pdf]

• Schepsmeier, U. and J. Stoeber (2013)
  Derivatives and Fisher information of bivariate copulas.
  Statistical Papers
  online first: http://link.springer.com/article/10.1007/s00362-013-0498-x.
  [pdf]
  Web supplement: Derivatives and Fisher Information of bivariate copulas.
  [pdf]
• Stoeber, J. and U. Schepsmeier (2013),
  Estimating standard errors in regular vine copula models
  (formerly: Is there significant time-variation in multivariate copulas?).
  Computational Statistics.
  online first: http://link.springer.com/article/10.1007/s00180-013-0423-8#
  [pdf]
• E.C. Brechmann and U. Schepsmeier (2013),
  Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine.
  Journal of Statistical Software, 52(3), 1-27.
  [pdf]
• Haff, I. H. (2013).
  Parameter estimation for pair copula construction.
  Bernoulli Journal, 19, 462-491 
  [pdf]
• Czado, C., Schepsmeier, U., Min, A. (2012)
  Maximum likelihood estimation of mixed C-vines with application to exchange rates
  Statistical Modelling, 12 (3), 229-255
  [pdf]

• Panagiotelis, A., Czado, C. and Joe, H. (2012)
  Pair copula constructions for multivariate discrete data. 
  J Amer Stat Assoc, 107:499, 1063-1072
  [pdf]
• Stöber, J., Hong, H., Czado, C., Ghosh, P (2012)
  Comorbidity of chronic diseases in the elderly: longitudinal patterns identified by a copula design for mixed responses.
  Submitted for publication.

• Kauermann, G. and Schellhase, C. (2013)
  Flexible pair-copula estimation in D-vines with Penalized Splines
  preprint.
• Schellhase, C. and Kauermann, G. (2013)
  Flexible pair-copula estimation in R-vines for portfolio optimization
  working paper.
• Hobaek Haff, I. and Segers, J. (2012)
  Nonparametric estimation of pair-copula constructions with the empirical pair-copula
  preprint.
  [pdf]

• Bauer, A. and C. Czado (2012)
  Pair-copula Bayesian networks
  Submitted for publication
  [link]
• Bauer, A., Czado, C. and Klein, T. (2012)
  Pair-copula constructions for non-Gaussian DAG models.
  Canadian Journal of Statistics, 40 (1), 86-109
  [pdf]

• Nikoloulopoulos, A.K., Joe, H., and Li, H.  (2012)
  Vine copulas with asymmetric tail dependence and applications to financial return data.
  Computational Statistics and Data Analysis, 56 (11), 3659-3673
  [pdf]
• Joe, H., Li, H. and Nikoloulopoulos, A.K.  (2010)
  Tail dependence functions and vine copulas.
  Journal of Multivariate Analysis, 101, 252-270.
  [pdf]

• Almeida, C., C. Czado and H. Manner (2012)
  Modeling high dimensional time-varying dependence using D-vine SCAR models
  Submitted for publication
  [link]
• Stoeber, J. and C. Czado (2011),
  Detecting regime switches in the dependence structure of high dimensional financial data.
  forthcoming in Computational Statistics and Data Analysis.
  [pdf]

• Brechmann, E.C. and Czado, C. (2012),
  COPAR - Multivariate Time Series Modeling Using the COPula AutoRegressive Model.
  Submitted for publication.
  [pdf]

• Schmidl, D., Czado, C., Hug, S., and Theis, F. J. (2013)
  A vine-copula based adaptive MCMC sampler for efficient inference of dynamical systems.
  Bayesian Analysis, 8(1), 1-22

• E.C. Brechmann, C. Czado and S. Paterlini (2013),
  Flexible Dependence Modeling of Operational Risk Losses and Its Impact on Total Capital Requirements.
  preprint
  [pdf]
• E.C. Brechmann, K. Hendrich and C. Czado (2013),
  Conditional Copula Simulation for Systemic Risk Stress Testing.
  preprint
  [pdf]
  
• Brechmann, E.C. and C. Czado (2013),
  Risk Management with High-Dimensional Vine Copulas: An Analysis of the Euro Stoxx 50.
  Statistics & Risk Modeling, to appear.
  [pdf]
• Min, A. and Czado, C. (2012),
  SCOMDY models based on pair-copula constructions with application to exchange rates.
  to appear in: Computational Statistics and Data Analysis
  online first: http://dx.doi.org/10.1016/j.csda.2012.08.003
  [link]
• Hofmann, M. and Czado, C. (2010),
  Assessing the VaR of a portfolio using D-vine copula based multivariate GARCH models
  Submitted for publication.
  [pdf]

• Krämer, N, Brechmann, E.C., Silvestrini, D. and Czado, C. (2012),
  Total loss estimation using copula-based regression models
  Submitted for publication.
  [link]
• Erhardt, V. and Czado, C. (2012)
  Modeling dependent yearly claim totals including zero claims in private health insurance.
  Scandinavian Actuarial Journal, 2, 106-129
  [link]

• Czado, C., Gärtner, F. and Min, A. (2011)
  Analysis of Australian electricity loads using joint Bayesian inference of D-Vines with autoregressive margins
  (Handbook on Vines, Editors: Dorota Kurowicka and Harry Joe, World Scientific)

VineCopula: Statistical inference of vine copulas

This package provides functions for statistical inference of vine copulas. It contains tools for bivariate exploratory data analysis, bivariate copula selection and (vine) tree construction. Models can be estimated either sequentially or by joint maximum likelihood estimation. Sampling algorithms and plotting methods are also included. Data is assumed to lie in the unit hypercube (so-called copula data). For C- and D-vines links to the package CDVine are provided.

• http://cran.r-project.org/web/packages/VineCopula/
• Manual [pdf]

CDVine: Statistical inference of C- and D-vine copulas

This package provides functions for statistical inference of canonical vine (C-vine) and D-vine copulas. It contains tools for bivariate exploratory data analysis and for bivariate as well as vine copula selection. Models can be estimated either sequentially or by joint maximum likelihood estimation. Sampling algorithms and plotting methods are also included. 

• http://cran.r-project.org/web/packages/CDVine/
• Presentation at the 4th Workshop on Vine Copula Distributions and Applications, TU München [pdf]
• Package vignette: [pdf]
• Manual [pdf]

Unicorn

The "Uncertainty analysis with Correlations" (UNICORN) software tool, implementing staff research work on dependence modelling for high dimensional distributions. It uses dependence trees and regular vines with diagonal band, maximum entropy and elliptical copulae.

Homepage at TU Delft (Netherlands): http://risk2.ewi.tudelft.nl/oursoftware/3-unicorn

• Nonparametric estimation of Pair Copula Constructions (PCCs)
  (Nicole Krämer, Claudia Czado)
• Vine copula networks
  (Eike Brechmann, Claudia Czado) 
• Bayesian model selection and estimation
  (Lutz Gruber, Claudia Czado)
• Goodness-of-fit test for R-vines
  (Ulf Schepsmeier)