Particle Rolling MCMC

An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC)with double block sampling. In our method, which is based on Sequential Monte Carlo(SMC), particles are sequentially updated to approximate the posterior distribution foreach window by learning new information and discarding old information from obser-vations. Th particles are refreshed with an MCMC algorithm when the importanceweights degenerate. To avoid degeneracy, which is crucial for reducing the computation time, we introduce a block sampling scheme and generate multiple candidates bythe algorithm based on the conditional SMC. The theoretical discussion shows thatthe proposed methodology with a nested structure is expressed as SMC sampling forthe augmented space to provide the justification. The computational performance isevaluated in illustrative examples, showing that the posterior distributions of the modelparameters are accurately estimated. The proofs and additional discussions (algorithmsand experimental results) are provided in the Supplementary Material.