This page provides an extensive overview 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. 

Slides

• 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]
 

• 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]
  
  

• 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]
• 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]
• Panagiotelis, A., Czado, C. and Joe, H. (2012)
  Pair copula constructions for multivariate discrete data.
  J Amer Stat Assoc, 107:499, 1063-1072
  [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]
• 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]
• 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]
• 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]
• 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., 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)
• 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]
• 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]
• Joe, H., Li, H. and Nikoloulopoulos, A.K.  (2010)
  Tail dependence functions and vine copulas.
  Journal of Multivariate Analysis, 101, 252-270.
  [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]
  
  

• Czado, C., S. Jeske and M. Hofmann (2012)
  Selection strategies for regular vine copulae
  Submitted for publication
  [link]
• Bauer, A. and C. Czado (2012)
  Pair-copula Bayesian networks
  Submitted for publication
  [link]
• Krämer, N, Brechmann, E.C., Silvestrini, D. and Czado, C. (2012),
  Total loss estimation using copula-based regression models.
  Submitted for publication.
  [link]
• Stoeber, J. and U. Schepsmeier (2012),
  Estimating standard errors in regular vine copula models
  (formerly: Is there significant time-variation in multivariate copulas?).
  Submitted for publication.
  [pdf]
• Stoeber, J.,  H. Joe and C. Czado (2012),
  Simplified Pair Copula Constructions - Limits and Extensions.
  Submitted for publication.
  [pdf]
• Almeida, C., C. Czado and H. Manner (2012)
  Modeling high dimensional time-varying dependence using D-vine SCAR models
  Submitted for publication
  [link]
• Brechmann, E.C. and C. Czado (2012),
  COPAR - Multivariate Time Series Modeling Using the COPula AutoRegressive Model.
  Submitted for publication.
  [pdf]
• Haff, I. H. (2011).
  Parameter estimation for pair copula construction.
  to appear in: Bernoulli Journal
  [pdf]
• Brechmann, E.C. and C. Czado (2011),
  Risk Management with High-Dimensional Vine Copulas: An Analysis of the Euro Stoxx 50.
  Submitted for publication.
  [pdf]
• Stoeber, J. and C. Czado (2011),
  Detecting regime switches in the dependence structure of high dimensional financial data.
  Submitted for publication.
  [pdf]
• Hofmann, M. and Czado, C. (2010)
  Assessing the VaR of a portfolio using D-vine copula based multivariate GARCH models
  Submitted for publication.
  [pdf]
  
  

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

• Pair-copula constructions for non-Gaussian DAG models
  (Alexander Bauer, Claudia Czado, Thomas Klein)
• Nonparametric estimation of Pair Copula Constructions (PCCs)
  (Nicole Krämer, Claudia Czado)
• Time varying vine copula models
  (Jakob Stöber, Claudia Czado)
• Bayesian inference for stochastic time-varying copula models 
  (Carlos Almeida, Claudia Czado)
• Vine copula networks
  (Eike Brechmann, Claudia Czado) 
• Copula Discriminant Analysis
  (Nicole Krämer, Claudia Czado)
• Regression model based on vines
  (Nicole Krämer, Jakob Stöber, Ulf Schepsmeier, Claudia Czado)
• Bayesian model selection and estimation
  (Lutz Gruber, Jakob Stöber, Claudia Czado)
• Fisher Information, Hessian Matrix and standard errors for R-vines
  (Jakob Stöber, Ulf Schepsmeier)
• Goodness-of-fit test for R-vines
  (Ulf Schepsmeier)