Robust Recursive Filtering and Smoothing

Using a perturbation approach, we derive a new approximate filtering and smoothing methodology for a general class of state-space models including univariate and multivariate location, scale, and count data models. The main properties of the methodology can be summarized as follows: (i) it generalizes several existing approaches to robust filtering based on the score and the Hessian matrix of the observation density by relaxing the critical assumption of a Gaussian prior density underlying this class of methods; (ii) has a very simple structure based on forward-backward recursions similar to the Kalman filter and smoother; (iii) allows a straightforward computation of confidence bands around the state estimates reflecting the combination of parameter and filtering uncertainty. We show through an extensive Monte Carlo study that the mean square loss with respect to exact simulation-based methods is small in a wide range of scenarios. We finally illustrate empirically the application of the methodology to the estimation of stochastic volatility and correlations in financial time-series.