R-vine tree methods

  • 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]
  • Cooke, R. M., Kurowicka, D., & Wilson, K. (2015)
    Sampling, Conditionalizing, Counting, Merging, Searching Regular Vines
    Journal of Multivariate Analysis 138, 4-18.
    [link]

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Simplified and non-simplified vines

  • Kurz, M. and Spanhel, F. (2017)
    Testing the simplifying assumption in high-dimensional vine copulas
    submitted
    [preprint]
  • Vatter, T. and Nagler, T. (2016)
    Generalized additive models for pair-copula constructions
    Submitted
    [preprint]
  • Killiches, M., Kraus, D. and Czado, C. (2016)
    Examination and visualization of the simplifying assumption for vine copulas in three dimensions
    Australian and New Zealand Journal of Statistics
    [preprint]
  • Spanhel, F. and Kurz, M. (2015)
    Simplified vine copula models: Approximations based on the simplifying assumption
    [preprint]
  • Stöber, 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]
  • Acar, E., Genest, C. and Nešlehová, J. (2012)
    Beyond simplified pair-copula constructions
    Journal of Multivariate Analysis, 110, 74-90.
    [link]
  • 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]

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Model selection

  • Kraus, D. and Czado, C. (2017)
    Growing simplified vine copula trees: improving Dißmann's algorithm
    submitted for publication
    [preprint]
  • Killiches, M., Kraus, D. and Czado, C. (2017)
    Model distances for vine copulas in high dimensions.
    Statistics and Computing (doi:10.1007/s11222-017-9733-y)
    [preprint]
  • Müller, D. and Czado, C. (2017)
    Selection of Sparse Vine Copulas in High Dimensions with the Lasso
    submitted for publication
    [preprint]
  • Killiches, M., Kraus, D. and Czado, C. (2016)
    Using model distances to investigate the simplifying assumption, goodness-of-fit and truncation levels for vine copulas.
    submitted for publication
    [preprint]
  • Prokhorov, A., Schepsmeier, U. and Zhu, Y. (2016)
    Generalized Information Matrix Tests for Copulas.
    under review in Journal of Multivariate Analysis
  • Schepsmeier, U. (2016)
    A goodness-of-fit test for regular vine copula models.

    accepted in Economic Reviews

    [pdf]
  • Schepsmeier, U. (2015)
    Efficient information based goodness-of-fi t tests for vine copula models with fixed margins.
    Journal of Multivariate Analysis 138, 34-52.
    (formerly: Efficient goodness-of-fit tests in multi-dimensional vine copula models)
    [pdf]
  • Brechmann, E. and Joe, H. (2015)
    Truncation of vine copulas using fit indices.

    Journal of Multivariate Analysis 138, 19-33.

    [pdf]
  • Gruber, L. and Czado, C. (2015)
    Sequential Bayesian Model Selection of Regular Vine Copulas
    .
    Bayesian Anal. Volume 10, Number 4 (2015), 937-963.
  • 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., Jeske, S., & Hofmann, M. (2013).
    Selection strategies for regular vine copulae.

    Journal de la Société Française de Statistique
    , 154(1), 174-191.
    [pdf]
  • 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]

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Computation and Estimation

  • Schepsmeier, U. and J. Stöber (2014)
    Derivatives and Fisher information of bivariate copulas.
    Statistical Papers, 55(2), 525-542.
    online first: http://link.springer.com/article/10.1007/s00362-013-0498-x.
    [pdf]
    Web supplement: Derivatives and Fisher Information of bivariate copulas.
    [pdf]
  • Stöber, J. and U. Schepsmeier (2013)
    Estimating standard errors in regular vine copula models
    Computational Statistics, 28 (6), 2679-2707
    [link]
  • 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]

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Discrete and discrete/continuous vines

  • Panagiotelis, A., Czado, C. Joe, H. and Stöber, J. (2017)
    Model selection for discrete regular vine copulas.
    Computational Statistics & Data Analysis, Volume 106, Pages 138–152
    [preprint]
  • Panagiotelis, A., Czado, C. and Joe, H. (2012)
    Pair copula constructions for multivariate discrete data. 
    J Amer Stat Assoc, 107:499, 1063-1072
    [link] [pdf]
  • Stöber, J., Hong, H., Czado, C., Ghosh, P (2015)
    Comorbidity of chronic diseases in the elderly: longitudinal patterns identified by a copula design for mixed responses.
    Computational Statistics & Data Analysis, Volume 88, Pages 28–39.
    [preprint]

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Vines with non-parametric pair-copulas

  • Christian Schellhase, Fabian Spanhel (2017)
    Estimating Non-Simplified Vine Copulas Using Penalized Splines.
    Statistics & Computing (doi: 10.1007/s11222-017-9737-7)
    [preprint]
  • Nagler T., Schellhase, C. and Czado, C. (2016)
    Nonparametric estimation of simplified vine copula models: comparison of methods
    Submitted
    [preprint]
  • Nagler, T. and Czado, C. (2016)
    Evading the curse of dimensionality in multivariate kernel density estimation with simplified vines.
    Journal of Multivariate Analysis 151, 69-89 (doi:10.1016/j.jmva.2016.07.003)
    [preprint]
  • Hobaek Haff, I. and Segers, J. (2015)
    Nonparametric estimation of pair-copula constructions with the empirical pair-copula.
    Computational Statistics & Data Analysis, Volume 84, Pages 1–13.
    [pdf]
  • Kauermann, G. and Schellhase, C. (2013)
    Flexible pair-copula estimation in D-vines with Penalized Splines.
    Statistics and Computing, Volume 24(6), Pages 1081-1100 (doi: 10.1007/s11222-013-9421-5)
    [link]
  • Schellhase, C. and Kauermann, G. (2013)
    Flexible pair-copula estimation in R-vines for portfolio optimization.
    working paper

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DAG models

  • Müller, D. and Czado, C. (2016)
    Representing sparse Gaussian DAGs as sparse R-vines allowing for non-Gaussian dependence
    submitted for publication
    [preprint]
  • Bauer, A. and C. Czado (2015)
    Pair-copula Bayesian networks
    Journal of Computational and Graphical Statistics
    [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]

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Tail dependence

  • 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]
  • Jaworski, P. (2015)
    Univariate conditioning of vine copulas.
    Journal of Multivariate Analysis, 138, 89-103.
    [link]

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Time-varying Vine Copulas

  • Fink, H., Y. Klimova, C. Czado J. and Stöber (2017)
    Regime switching vine copula models for global equity and volatility indices
    Econometrics 2017, 5, 3; doi:10.3390/econometrics5010003
    [link][preprint]
  • Almeida, C., C. Czado and H. Manner (2016)
    Modeling high-dimensional time-varying dependence using dynamic D-vine models
    Applied Stochastic Models in Business and Industry 2016.
    [link][preprint]
  • Stöber, J. and C. Czado (2014),
    Detecting regime switches in the dependence structure of high dimensional financial data.
    Computational Statistics & Data Analysis, 76, 672-686.
    [link]

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Time series analysis

  • Smith, M. and Vahey, S. (2015)
    Asymmetric Density Forcasting of U.S. Macroeconomic Variables using a Gaussian Copula Model of Cross-Sectional and Serial Dependence.
    [preprint]
  • Smith, M. (2014)
    Copula Modelling of Dependence in Multivariate Time Series.
    International Journal of Forecasting, Volume 31, Issue 3, Pages 815–833
    [link] [preprint]
  • Brechmann, E.C. and Czado, C. (2014),
    COPAR - Multivariate Time Series Modeling Using the COPula AutoRegressive Model.

    Applied Stochastic Models in Business and Industry, Volume 31, Issue 4, Pages 495–514.

    [link]

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Acceleration of MCMC algorithms

  • 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

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Spatial vine copulas

  • Pereira, G., Veiga, A., Erhardt, T. M., and C. Czado (2017)
    A periodic spatial vine copula model for multi-site streamflow simulation.
    Electric Power Systems Research, 152, 9-17
    [link]
  • Erhardt, T. M. and Czado, C. (2015)
    Standardized drought indices: A novel uni- and multivariate approach
    [preprint]
  • Erhardt, T. M., Czado, C. and Schepsmeier, U. (2015)
    Spatial composite likelihood inference using local C-vines.
    Journal of Multivariate Analysis 138, 74-88
    [preprint][link]
  • Erhardt, T. M., Czado, C. and Schepsmeier, U. (2015)
    R-vine Models for Spatial Time Series with an Application to Daily Mean Temperature.
    Biometrics 71, 323-332
    [preprint][link]
  • Gräler, B. (2014)
    Modelling Skewed Spatial Random Fields through the Spatial Vine Copula.
    Spatial Statistics 10, 87 - 102.
    [link]
  • Gräler, B. and Pebesma, E. (2012)
    Modelling Dependence in Space and Time with Vine Copulas.
    Presentation at: Geostats 2012, Oslo, Norway, 11-15 June 2012
    [link]
  • Gräler, B. and Pebesma, E. (2011)
    The pair-copula construction for spatial data: a new approach to model spatial dependency.
    Procedia Environmental Sciences 7, 206-211.
    [pdf]

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Block maxima

  • Killiches, M. and Czado, C. (2015)
    Block-Maxima of Vines.
    To appear in Extreme Value Modelling and Risk Analysis: Methods and Applications. Eds. D. Dey and J. Yan. Chapman & Hall/CRC Press.
    [preprint]

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Factor models with vines

  • Schamberger, B., Gruber, L. and C. Czado (2017)
    Bayesian Inference for Latent Factor Copulas and Application to Financial Risk Forecasting
    Econometrics 2017, 5, 21; doi:10.3390/econometrics5020021
    [pdf]
  • Krupskii, P. and Joe, H. (2013).
    Factor copula models for multivariate data,
    Journal of Multivariate Analysis, 120, 85-101.

    [pdf]
  • Nikoloulopoulos, A. and Joe, H. (2013).
    Factor copula models for item response data.

    Psychometrika, 1-25.
    [link]
  • Krupskii, P., & Joe, H. (2015).
    Structured factor copula models: Theory, inference and computation.
    Journal of Multivariate Analysis 138, 53-73.

    [link]

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Applications

Econometrics

  • Sriboonchitta, S., Kosheleva, O. and Nguyen, H. T.
    Why Are Vine Copulas So Successful in Econometrics?
    [pdf]

Finance

  • Ivanov, E., Min, A. and F. Ramsauer (2017)
    Copula-Based Factor Models for Multivariate Asset Returns
    Econometrics 2017, 5, 20; doi:10.3390/econometrics5020020
    [pdf]
  • M. Fischer, D. Kraus, M. Pfeuffer and C. Czado (2017)
    Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression
    Risks 2017, 5(3), 38.
    [preprint]
  • Maya, R. A. L., Gomez-Gonzales, J. E. and Velandia, L. F. M. (2015)
    Latin American Exchange Rate Dependencies: A Regular Vine Copula Approach
    Contemporary Economic Policy, Volume 33, Issue 3, 535–549.
    [link]
  • E.C. Brechmann, C. Czado and S. Paterlini (2014),
    Flexible Dependence Modeling of Operational Risk Losses and Its Impact on Total Capital Requirements.
    Journal of Banking & Finance, 40, 271-285.
    [pdf][link]
  • E.C. Brechmann, C. Czado and S. Paterlini (2013),
    Modeling Dependence of Operational Loss Frequencies.
    Journal of Operational Risk, 8(4), 105-126.
    [link]
  • Brechmann, E.C., K. Hendrich and C. Czado (2013)
    Conditional copula simulation for systemic risk stress testing.
    Insurance: Mathematics and Economics, 53, 722-732
    [pdf][link]
  • Brechmann, E.C. and C. Czado (2013),
    Risk Management with High-Dimensional Vine Copulas: An Analysis of the Euro Stoxx 50.
    Statistics & Risk Modeling, 30(4), 307-342.
    [pdf]
  • Min, A. and Czado, C. (2014),
    SCOMDY models based on pair-copula constructions with application to exchange rates.
    Computational Statistics and Data Analysis, 76, 523-535.
    [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]

Insurance

  • Krämer, N, Brechmann, E.C., Silvestrini, D. and Czado, C. (2013),
    Total loss estimation using copula-based regression models
    Insurance: Mathematics and Economics, 53, 829-839
    [preprint][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]

Energy

  • 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)

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Parsimonious and structured vines

  • E.C. Brechmann and H. Joe (2014).
    Parsimonious Parameterization of Correlation Matrices Using Truncated Vines and Factor Analysis
    .
    Computational Statistics & Data Analysis, Volume 77, Pages 233–251.
    [pdf] [link]

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Regression methods

  • Kraus, D., and Czado, C. (2017)
    D-vine Copula Based Quantile Regression
    Computational Statistics and Data Analysis, 110, 1-18
    [preprint]
  • Cooke, R. M., Joe, H. and Chang, B. (2015)
    Vine Regression.
    Resources for the Future - Discussion Paper, 15-52.
    [link]
  • Schallhorn, N., Kraus, D., Nagler, T. and Czado, C. (2017)
    D-vine quantile regression with discrete variables
    submitted for publication
    [preprint]

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Alternative multivariate copula models

  • E.C. Brechmann (2014)
    Hierarchical Kendall Copulas: Properties and Inference.

    Canadian Journal of Statistics, 42(1), 78-108.
    [link]
  • E.C. Brechmann (2013)
    Sampling from Hierarchical Kendall Copulas.

    Journal de la Société Française de Statistique, 154(1), 192-209.
    [link]

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Survival Analysis

  • Barthel, N., Geerdens, C., Killiches, M., Janssen, P. and Czado, C. (2017)
    Vine copula based likelihood estimation of dependence patterns in multivariate event time data.
    Computational Statistics & Data Analysis, doi.org/10.1016/j.csda.2017.07.010.
    [link]

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Survey Papers

  • Aas, K. (2016)
    Pair-Copula Constructions for Financial Applications: A Review.
    Econometrics 2016, 4, 43.
    [link]

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