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.
Highlights
IntroductionIt is necessary to model both the serial dependence and the dependence between different time series
In many financial applications, it is necessary to model both the serial dependence and the dependence between different time series
We aim to extend the results of these authors to find the asymptotic behavior of sequential empirical processes constructed from the residuals of multivariate stochastic volatility models
Summary
It is necessary to model both the serial dependence and the dependence between different time series. Using a multivariate GARCH-like model with diagonal stochastic volatility matrices, Chen and Fan [10] showed the remarkable result that estimating the copula parameters using the rank-based maximum pseudo-likelihood method [11,12]. This is the case in Chen and Fan [10]. The main results are proved in a series of Appendices
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