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Vine Copula Specifications for Stationary Multivariate Markov Chains

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  • Brendan K. Beare
  • Juwon Seo

Abstract

type="main" xml:id="jtsa12103-abs-0001"> Vine copulae provide a graphical framework in which multiple bivariate copulae may be combined in a consistent fashion to yield a more complex multivariate copula. In this article, we discuss the use of vine copulae to build flexible semiparametric models for stationary multivariate higher-order Markov chains. We propose a new vine structure, the M-vine, that is particularly well suited to this purpose. Stationarity may be imposed by requiring the equality of certain copulae in the M-vine, while the Markov property may be imposed by requiring certain copulae to be independence copulae.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:2:p:228-246
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    Cited by:

    1. Simard Clarence & Rémillard Bruno, 2015. "Forecasting time series with multivariate copulas," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-24, May.
    2. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    3. Shulin Zhang & Qian M. Zhou & Huazhen Lin, 2021. "Goodness-of-fit test of copula functions for semi-parametric univariate time series models," Statistical Papers, Springer, vol. 62(4), pages 1697-1721, August.
    4. Martin Bladt & Alexander J. McNeil, 2020. "Time series copula models using d-vines and v-transforms," Papers 2006.11088, arXiv.org, revised Jul 2021.
    5. 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.
    6. 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.
    7. Begin, Étienne & Dutilleul, Pierre & Beaulieu, Carole & Bouezmarni, Taoufik, 2020. "M-Vine decomposition and VAR(1) models," Statistics & Probability Letters, Elsevier, vol. 158(C).
    8. 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.
    9. Jang, Hyuna & Kim, Jong-Min & Noh, Hohsuk, 2022. "Vine copula Granger causality in mean," Economic Modelling, Elsevier, vol. 109(C).
    10. Chen, Xiaohong & Xiao, Zhijie & Wang, Bo, 2022. "Copula-based time series with filtered nonstationarity," Journal of Econometrics, Elsevier, vol. 228(1), pages 127-155.
    11. Overbeck Ludger & Schmidt Wolfgang M., 2015. "Multivariate Markov Families of Copulas," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-13, October.
    12. Ruben Loaiza-Maya & Michael Stanley Smith, 2017. "Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series," Papers 1712.09150, arXiv.org, revised Jul 2018.
    13. Guilherme Armando Almeida Pereira & Álvaro Veiga, 2019. "Periodic Copula Autoregressive Model Designed to Multivariate Streamflow Time Series Modelling," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(10), pages 3417-3431, August.
    14. Martin Bladt & Alexander J. McNeil, 2021. "Time series models with infinite-order partial copula dependence," Papers 2107.00960, arXiv.org.
    15. Yousaf Ali Khan, 2022. "Modeling Dependent Structure Among Micro-Economics Variables Through COPAR (1)-Model in Pakistan," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 257-279, March.
    16. Huang, Wanling & Mollick, André Varella & Nguyen, Khoa Huu, 2016. "U.S. stock markets and the role of real interest rates," The Quarterly Review of Economics and Finance, Elsevier, vol. 59(C), pages 231-242.
    17. Smith, Michael Stanley & Maneesoonthorn, Worapree, 2018. "Inversion copulas from nonlinear state space models with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 34(3), pages 389-407.
    18. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Czado, Claudia & Ivanov, Eugen & Okhrin, Yarema, 2019. "Modelling temporal dependence of realized variances with vines," Econometrics and Statistics, Elsevier, vol. 12(C), pages 198-216.
    20. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    21. Bladt, Martin & McNeil, Alexander J., 2022. "Time series copula models using d-vines and v-transforms," Econometrics and Statistics, Elsevier, vol. 24(C), pages 27-48.
    22. Eugen Ivanov & Aleksey Min & Franz Ramsauer, 2017. "Copula-Based Factor Models for Multivariate Asset Returns," Econometrics, MDPI, vol. 5(2), pages 1-24, May.
    23. Bladt Martin & McNeil Alexander J., 2022. "Time series with infinite-order partial copula dependence," Dependence Modeling, De Gruyter, vol. 10(1), pages 87-107, January.
    24. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.

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