Quantile Filtering and Learning

Quantile and least-absolute deviations (LAD) methods are popular robust statistical methods but have not generally been applied to state filtering and sequential parameter learning. This paper introduces robust state space models whose error structure coincides with quantile estimation criterion, with LAD a special case. We develop an efficient particle based method for sequential state and parameter inference. Existing approaches focus solely on the problem of state filtering, conditional on parameter values. Our approach allows for sequential hypothesis testing and model monitoring by computing marginal likelihoods and Bayes factors sequentially through time. We illustrate our approach with a number of applications with real and simulated data. In all cases we compare our results with existing algorithms where possible and document the efficiency of our methodology.