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Stationary vine copula models for multivariate time series

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  • Nagler, Thomas
  • Krüger, Daniel
  • Min, Aleksey

Abstract

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The theoretical results allow for misspecified models and, even when specialized to the iid case, go beyond what is available in the literature. The new model class is illustrated by an application to forecasting returns of a portfolio of 20 stocks, where they show excellent forecast performance. The paper is accompanied by an open source software implementation.

Suggested Citation

  • Nagler, Thomas & Krüger, Daniel & Min, Aleksey, 2022. "Stationary vine copula models for multivariate time series," Journal of Econometrics, Elsevier, vol. 227(2), pages 305-324.
    • Handle: RePEc:eee:econom:v:227:y:2022:i:2:p:305-324
    DOI: 10.1016/j.jeconom.2021.11.015
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    1. Jinguo Gong & Yadong Li & Liang Peng & Qiwei Yao, 2015. "Estimation of extreme quantiles for functions of dependent random variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(5), pages 1001-1024, November.
    2. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    3. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    4. Nasri, Bouchra R. & Rémillard, Bruno N. & Bouezmarni, Taoufik, 2019. "Semi-parametric copula-based models under non-stationarity," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 347-365.
    5. Axel Bücher & Ivan Kojadinovic, 2019. "A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1145-1165, September.
    6. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, vol. 4(4), pages 1-15, October.
    7. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
    8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    9. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
    10. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    11. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    12. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    13. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    14. Rubén Loaiza‐Maya & Michael S. Smith & Worapree Maneesoonthorn, 2018. "Time series copulas for heteroskedastic data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 332-354, April.
    15. Xiaohong Chen & Zhijie Xiao & Bo Wang, 2020. "Copula-Based Time Series With Filtered Nonstationarity," Cowles Foundation Discussion Papers 2242, Cowles Foundation for Research in Economics, Yale University.
    16. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
    17. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    18. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    19. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    20. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(3), pages 819-846, June.
    21. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    22. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    23. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    24. Nasri, Bouchra R. & Rémillard, Bruno N., 2019. "Copula-based dynamic models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 107-121.
    25. Pfaff, Bernhard, 2008. "VAR, SVAR and SVEC Models: Implementation Within R Package vars," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i04).
    26. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    27. Longla, Martial & Peligrad, Magda, 2012. "Some aspects of modeling dependence in copula-based Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 234-240.
    28. Chen, Xiaohong & Huang, Zhuo & Yi, Yanping, 2021. "Efficient estimation of multivariate semi-nonparametric GARCH filtered copula models," Journal of Econometrics, Elsevier, vol. 222(1), pages 484-501.
    29. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    30. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
    31. Ibragimov, Rustam & Müller, Ulrich K., 2010. "t-Statistic Based Correlation and Heterogeneity Robust Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 453-468.
    32. Eike Christian Brechmann & Claudia Czado, 2015. "COPAR—multivariate time series modeling using the copula autoregressive model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(4), pages 495-514, July.
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