Abstract

In this paper, we introduce a new sequential Monte Carlo method, the state-observation sampling (SOS) filter. SOS extends the particle filtering methodology to general state-space models where the density of the observation conditional on the state is unavailable. In the mutation stage of SOS, a set of state-observation pairs are sampled from pas(with Laurent Calvet) t state particles. In the importance sampling step, each state particle is weighted by the kernel distance between its corresponding simulated observation and the actual data point. We establish that the convergence rate of SOS coincides with the convergence rate of a kernel density estimator on the observation space. SOS overcomes the curse of dimensionality with respect to the size of state space. We develop a plug-in rule for the selection of the bandwidth. The good finite-sample performance of SOS is demonstrated on an asset pricing model with investor learning.

Joint work with Laurent Calvet.