Particle Filtering and Parameter Learning

In this paper, we provide an exact particle filtering and parameter learning algorithm. Our approach exactly samples from a particle approximation to the joint posterior distribution of both parameters and latent states, thus avoiding the use of and the degeneracies inherent to sequential importance sampling. Exact particle filtering algorithms for pure state filtering are also provided. We illustrate the efficiency of our approach by sequentially learning parameters and filtering states in two models. First, we analyze a robust linear state space model with t-distributed errors in both the observation and state equation. Second, we analyze a log-stochastic volatility model. Using both simulated and actual stock index return data, we find that algorithm efficiently learns all of the parameters and states in both models.