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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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    1. Stéphane Bonhomme & Jean-Marc Robin, 2009. "Assessing the Equalizing Force of Mobility Using Short Panels: France, 1990-2000," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 63-92.
    2. 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.
    3. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    4. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    5. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09j008g6g0g is not listed on IDEAS
    6. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
    7. P. Gagliardini & C. Gourieroux, 2008. "Duration time‐series models with proportional hazard," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 74-124, January.
    8. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(3), pages 819-846, June.
    9. Cornelia Savu & Wing Lon Ng, 2005. "The SCoD Model: Analyzing Durations with a Semiparametric Copula Approach," International Review of Finance, International Review of Finance Ltd., vol. 5(1‐2), pages 55-74, March.
    10. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    11. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    12. Sun, Jiafeng & Frees, Edward W. & Rosenberg, Marjorie A., 2008. "Heavy-tailed longitudinal data modeling using copulas," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 817-830, April.
    13. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
    14. 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.
    15. Lorraine Dearden & Emla Fitzsimons & Alissa Goodman & Greg Kaplan, 2008. "Higher Education Funding Reforms in England: The Distributional Effects and the Shifting Balance of Costs," Economic Journal, Royal Economic Society, vol. 118(526), pages 100-125, February.
    16. 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.
    17. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    18. Mehra Yash P, 2004. "The Output Gap, Expected Future Inflation and Inflation Dynamics: Another Look," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
    19. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    20. Smith, Michael & Min, Aleksey & Almeida, Carlos & Czado, Claudia, 2010. "Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial Dependence," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1467-1479.
    21. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    22. Yash P. Mehra, 2004. "The output gap, expected future inflation and inflation dynamics: another look," Working Paper 04-06, Federal Reserve Bank of Richmond.
    23. 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.
    24. Hobæk Haff, Ingrid, 2012. "Comparison of estimators for pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 91-105.
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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. Roberto Fuentes M. & Irene Crimaldi & Armando Rungi, 2024. "Non-linear dependence and Granger causality: A vine copula approach," Papers 2409.15070, arXiv.org.
    19. 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).
    20. 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.
    21. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    22. 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.
    23. Eugen Ivanov & Aleksey Min & Franz Ramsauer, 2017. "Copula-Based Factor Models for Multivariate Asset Returns," Econometrics, MDPI, vol. 5(2), pages 1-24, May.
    24. 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.
    25. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.

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