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Econometrics 2017, 5(1), 13; doi:10.3390/econometrics5010013

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

1
Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Côte Sainte-Catherine, Montréal(Québec), H3T 2A7, Canada
2
Groupe d’Études et de Recherche en Analyse des Décisions (GERAD), Montréal (Québec), H3T 2A7, Canada
3
Centre de Recherches Mathématiques (CRM), Montréal (Québec), H3C 3J7, Canada
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)
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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.
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Keywords: goodness-of-fit; time series; copulas; GARCH models goodness-of-fit; time series; copulas; GARCH models
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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

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