Sequential Monte Carlo Smoothing with Parameter Estimation

TL;DR

This paper introduces two novel Bayesian smoothing algorithms for state-space models with unknown parameters, improving joint smoothing and parameter estimation using Sequential Monte Carlo methods.

Contribution

The paper presents two new SMC-based Bayesian smoothing methods, including an adjustment to backward weights and a combined parameter learning approach, outperforming existing algorithms.

Findings

Effective on benchmark models with simulated data

Applied successfully to S&P 500 index returns during financial crisis

Outperforms existing SMC algorithms in joint smoothing and parameter estimation

Abstract

We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights. The second is a new method combining sequential parameter learning and smoothing algorithms for general state-space models. This method is straightforward but effective, and we find it is the best existing Sequential Monte Carlo algorithm to solve the joint Bayesian smoothing problem. We first illustrate the methods on three benchmark models using simulated data, and then apply them to a stochastic volatility model for daily S&P 500 index returns during the financial crisis.