Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-speciﬁc copula-based time series models oﬀers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspeciﬁcation of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model speciﬁcation testing of extreme conditional value-at-risk for ﬁnancial time series data.
Chen, Xiaohong; Koenker, Roger; and Xiao, Zhijie, "Copula-Based Nonlinear Quantile Autoregression" (2008). Cowles Foundation Discussion Papers. 1993.