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Open AccessArticle

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

by Bruno Rémillard 1,2,3
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
Econometrics 2017, 5(1), 13;
Received: 31 December 2016 / Revised: 7 March 2017 / Accepted: 8 March 2017 / Published: 17 March 2017
(This article belongs to the Special Issue Recent Developments in Copula Models)
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.
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Keywords: goodness-of-fit; time series; copulas; GARCH models goodness-of-fit; time series; copulas; GARCH models
MDPI and ACS Style

Rémillard, B. Goodness-of-Fit Tests for Copulas of Multivariate Time Series
. Econometrics 2017, 5, 13.

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