Dynamic quantile models

This paper introduces the Dynamic Additive Quantile (DAQ) model that ensures the monotonicity of conditional quantile estimates. The DAQ model is easily estimable and can be used for computation and updating of the Value-at-Risk. An asymptotically efficient estimator of the DAQ is obtained by maximizing an objective function based on the inverse KLIC measure. An alternative estimator proposed in the paper is the Method of L-Moments estimator (MLM). The MLM estimator is consistent, but generally not fully efficient. Goodness-of-fit tests and diagnostic tools for the assessment of the model are also provided. For illustration, the DAQ model is estimated from a series of returns on the Toronto Stock Exchange (TSX) market index.