Discussion Papers 2019

CIRJE-F-1110	"Particle rolling MCMC"
Author Name	Awaya, Naoki and Yasuhiro Omori
Date	January 2019
Full Paper	PDF file
Remarks	Revised version of CIRJE-F-1066 (2017) and CIRJE-F-1080 (2018) and CIRJE-F-1126 (2019).

Abstract
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 justications are provided for the proposed estimation methodology. As a special case, we obtain a new sequential MCMC based on Particle Gibbs. It is a exible method alternative to SMC2 that is based on Particle MH. The computational performance is evaluated in illustrative examples, showing that the posterior distributions of model parameters and marginal likelihoods are estimated with accuracy.

Abstract

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 justications are provided for the proposed estimation methodology. As a special case, we obtain a new sequential MCMC based on Particle Gibbs. It is a exible method alternative to SMC2 that is based on Particle MH. The computational performance is evaluated in illustrative examples, showing that the posterior distributions of model parameters and marginal likelihoods are estimated with accuracy.