Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 15 March 2017 / Approved: 16 March 2017 / Online: 16 March 2017 (09:38:24 CET)

A peer-reviewed article of this Preprint also exists.

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


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.


goodness-of-fit; time series; copulas; GARCH models


Business, Economics and Management, Econometrics and Statistics

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