Particle rolling MCMC with double-block sampling

TL;DR

This paper introduces a novel particle rolling MCMC method with double block sampling for efficient window estimation in state space models, improving accuracy and reducing degeneracy in sequential Monte Carlo procedures.

Contribution

The paper proposes a new particle rolling MCMC algorithm with double block sampling that enhances efficiency and accuracy in state space model estimation.

Findings

Accurately estimates posterior distributions of model parameters.

Reduces degeneracy in importance weights during sequential updates.

Demonstrates improved computational performance in illustrative examples.

Abstract

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 for each window by learning new information and discarding old information from observations. Th particles are refreshed with an MCMC algorithm when the importance weights degenerate. To avoid degeneracy, which is crucial for reducing the computation time, we introduce a block sampling scheme and generate multiple candidates by the algorithm based on the conditional SMC. The theoretical discussion shows that the proposed methodology with a nested structure is expressed as SMC sampling for the augmented space to provide the justification. The computational performance is evaluated in illustrative examples, showing that the posterior distributions of the model parameters are accurately estimated. The proofs and additional discussions (algorithms and experimental results) are provided in the Supplementary Material.