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Copula-based dynamic models for multivariate time series

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  • Nasri, Bouchra R.
  • Rémillard, Bruno N.

Abstract

In this paper, we propose an intuitive way to couple several dynamic time series models even when there are no innovations. This extends previous work for modeling dependence between innovations of stochastic volatility models. We consider time-dependent and time-independent copula models and we study the asymptotic behavior of some empirical processes constructed from pseudo-observations, as well as the behavior of maximum pseudo-likelihood estimators of the associated copula parameters. The results show that even if the univariate dynamic models depend on unknown parameters, the limiting behavior of many processes of interest does not depend on the estimation errors. One can perform tests for change points on the full distribution, the margins or the copula, as if the parameters of the dynamic models were known. This is also true for some parametric models of time-dependent copulas. This interesting property makes it possible to construct consistent tests of specification for the dependence models, without having to consider the dynamic time series models. Monte Carlo simulations are used to demonstrate the power of the proposed goodness-of-fit test in finite samples. An application to financial data is given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:172:y:2019:i:c:p:107-121
    DOI: 10.1016/j.jmva.2019.03.002
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    Citations

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    Cited by:

    1. 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.
    2. Andres Mauricio Molina Barreto & Naoyuki Ishimura, 2023. "Remarks on a copula‐based conditional value at risk for the portfolio problem," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 30(3), pages 150-170, July.
    3. Fulvia Pennoni & Francesco Bartolucci & Gianfranco Forte & Ferdinando Ametrano, 2022. "Exploring the dependencies among main cryptocurrency log‐returns: A hidden Markov model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(1), February.
    4. Nasri, Bouchra R. & Rémillard, Bruno N. & Bahraoui, Tarik, 2022. "Change-point problems for multivariate time series using pseudo-observations," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    5. 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.
    6. Marek Omelka & Šárka Hudecová & Natalie Neumeyer, 2021. "Maximum pseudo‐likelihood estimation based on estimated residuals in copula semiparametric models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1433-1473, December.
    7. Alessia Benevento & Fabrizio Durante, 2023. "Wasserstein Dissimilarity for Copula-Based Clustering of Time Series with Spatial Information," Mathematics, MDPI, vol. 12(1), pages 1-15, December.

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