CAViaR models for Value-at-Risk and Expected Shortfall with long range dependency features

We consider alternative specifications of conditional autoregressive quantile models to estimate Value-at-Risk and Expected Shortfall. The proposed specifications include a slow moving component in the quantile process, along with aggregate returns from heterogeneous horizons as regressors. Using data for 10 stock indices, we evaluate the performance of the models and find that the proposed features are useful in capturing tail dynamics better.