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A joint conditional autoregressive expectile and Expected Shortfall frameworkis proposed. The framework is extended through incorporating a measurementequation which models the contemporaneous dependence between the realizedmeasures and the latent conditional expectile. Nonlinear thresholdspecification is further incorporated into the proposed framework. A BayesianMarkov Chain Monte Carlo method is adapted for estimation, whose properties areassessed and compared with maximum likelihood via a simulation study.One-day-ahead VaR and ES forecasting studies, with seven market indices,provide empirical support to the proposed models.

Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected Shortfall