This paper analyses the recently suggested particle approach to filtering time series. We suggest that the alogrithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially undating prior distribution. Both problems are tackled in this paper. We believe we have largely solved the first problem and have reduced the order of magnitude of the second.
In addition we introduce the idea of stratification into the particle filter which allows us to perform on-line Bayesian calculations about the parameters which index the models and maximum likelihood estimation. The new methods are illustrated by using a stochastic volatility model and a time series model of angle.
Some Key Words: Filterning, Markov chain Monte Carlo, Particle filter, Simulation, SIR, State space