Particle rolling MCMC with double block sampling: conditional SMC update approach

An efficient simulation-based methodology is proposed for the rolling window esti- mation of state space models. Using the framework of the conditional sequential Monte Carlo update in the particle Markov chain Monte Carlo estimation, weighted particles are updated to learn and forget the information of new and old observations by the forward and backward block sampling with the particle simulation smoother. These particles are also propagated by the MCMC update step. Theoretical justifications are provided for the proposed estimation methodology. The computational performance is evaluated in illustrative examples, showing that the posterior distributions of model parameters and marginal likelihoods are estimated with accuracy. Finally, as a special case, our proposed method can be used as a new sequential MCMC based on Particle Gibbs, which is shown to outperform SMC2 that is the promising alternative method based on Particle MH in the simulation experiments.