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Goodness-of-Fit Tests for Copulas of Multivariate Time Series

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  • Bruno Rémillard

    (Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Côte Sainte-Catherine, Montréal(Québec), H3T 2A7, Canada
    Groupe d’Études et de Recherche en Analyse des Décisions (GERAD), Montréal (Québec), H3T 2A7, Canada
    Centre de Recherches Mathématiques (CRM), Montréal (Québec), H3C 3J7, Canada)

Abstract

In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations are discussed. It is also shown that if the stochastic volatility matrices are diagonal, which is the case if the univariate time series are estimated separately instead of being jointly estimated, then the empirical copula process behaves as if the innovations were observed; a remarkable property. As a by-product, one also obtains the asymptotic behavior of rank-based measures of dependence applied to residuals of these time series models.

Suggested Citation

  • Bruno Rémillard, 2017. "Goodness-of-Fit Tests for Copulas of Multivariate Time Series," Econometrics, MDPI, vol. 5(1), pages 1-23, March.
    • Handle: RePEc:gam:jecnmx:v:5:y:2017:i:1:p:13-:d:93377
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    References listed on IDEAS

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    Cited by:

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    2. Manner, Hans & Stark, Florian & Wied, Dominik, 2019. "Testing for structural breaks in factor copula models," Journal of Econometrics, Elsevier, vol. 208(2), pages 324-345.

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