STATISTICAL INFERENCE FOR MULTIVARIATE RESIDUAL COPULA OF GARCH MODELS

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Copula Methods for Forecasting Multivariate Time Series (2013, background): “Chen and Fan (2006b) and Chan et al. (2009) provided conditions under which the following asymptotic normal distribution is obtained: p T (̂T ) d !”
Simulated Method of Moments Estimation for Copula-Based Multivariate Models (2013, unknown): “A second popular method is semi-parametric MLE [see Genest, Ghoudi, and Rivest (1995) for iid data and Chen and Fan (2006), Chan et al. (2009), and Chen, Fan, and Tsyrennikov (2006) for time series data].”
Maximum likelihood estimation of mixed C-vines with application to exchange rates (2012, methodology): “To improve efficiency in the semi-parametric approach of Genest et al. (1995), Chen and Fan (2006) and Chan et al. (2009) based their inference for the copula parameters on the Kullback-Leibler information criteria.”
A review of copula models for economic time series (2012, methodology): “Chen and Fan [25] provided conditions under which an asymptotic normal distribution is obtained, and provide a method for estimating the asymptotic covariance matrix.”
Copulas in Econometrics (2014, methodology): “One surprising result in Chan et al. (2009) and Chen & Fan (2006a) in cases in which the marginal distributions are nonparametric is that under regularity conditions, the asymptotic distribution of the estimator of the copula parameter is not affected by the filtering step.”