Sequential Monte Carlo Smoothing with Parameter Estimation

Abstract

We propose two new sequential Monte Carlo (SMC) smoothing methods for general state-space models with unknown parameters. The first is a modification of the particle learning and smoothing (PLS) algorithm of Carvalho, Johannes, Lopes, and Polson (2010), with an adjustment in the backward resampling weights. The second, called Refiltering, is a two-stage method that combines sequential parameter learning and particle smoothing algorithms. We illustrate the methods on three benchmark models using simulated data, and apply them to a stochastic volatility model for daily S&P 500 index returns during the financial crisis. We show that both new methods outperform existing SMC approaches, and that Refiltering is competitive with smoothing approaches based on Markov chain Monte Carlo (MCMC) and Particle MCMC.