Robust Filtering

Filtering methods are powerful tools to estimate the hidden state of a state-space model from observations available in real time. However, they are known to be highly sensitive to the presence of small misspecifications of the underlying model and to outliers in the observation process. In this paper, we show that the methodology of robust statistics can be adapted to the framework of sequential filtering. We introduce an impact function that quantifies the sensitivity of the state distribution with respect to new data. Since the impact function of a standard filter is unbounded even in the simplest cases, we propose a filter with a bounded impact function which provides accurate state and parameter inference in the presence of model misspecifications. We illustrate its good properties in several examples including linear models and nonlinear financial models of stochastic volatility