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...

This paper provides an optimal filtering methodology in discretely observed continuous-time jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as...