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Semi-parametric copula-based models under non-stationarity

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

Abstract

In this paper, we consider non-stationary random vectors, where the marginal distributions and the associated copula may be time-dependent. We propose estimators for the unknown parameters and we establish the limiting distribution of the estimators of the copula and the conditional copula, together with a parametric bootstrap method for constructing confidence bands around the estimator and for testing the adequacy of the model. We also consider three examples of functionals of the copula-based model under non-stationarity: conditional quantiles, conditional means, and conditional expected shortfalls. The asymptotic distribution of the estimation errors is shown to be Gaussian, and bootstrapping methods are proposed to estimate their asymptotic variances. The finite-sample performance of our estimators is investigated through Monte Carlo experiments, and we give three examples of implementation of the proposed methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:347-365
    DOI: 10.1016/j.jmva.2019.03.007
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    References listed on IDEAS

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    10. Hohsuk Noh & Anouar El Ghouch & Taoufik Bouezmarni, 2013. "Copula-Based Regression Estimation and Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 676-688, June.
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    2. 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.
    3. Nasri, Bouchra R., 2020. "On non-central squared copulas," Statistics & Probability Letters, Elsevier, vol. 161(C).
    4. Alexandra Dias, 2024. "Maximum Pseudo-Likelihood Estimation of Copula Models and Moments of Order Statistics," Risks, MDPI, vol. 12(1), pages 1-26, January.
    5. Antoine Bergeron & Pierre Dutilleul & Carole Beaulieu & Taoufik Bouezmarni, 2022. "Dynamic Copulas for Monotonic Dependence Change in Time Series," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 683-693, November.

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