Sequential Monte Carlo Smoothing with Parameter Estimation

Biao Yang, Jonathan R. Stroud and Gabriel Huerta

George Washington University, Georgetown University and University of New Mexico

December 2017 (first version: April 2016)

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 algorithm (PLS) algorithm of Carvalho, Johannes, Lopes and Polson (2010), with an adjustment in the backwards 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 the Refiltering is competitive with smoothing approaches based on Markov chain Monte Carlo (MCMC) and Particle MCMC methods.

The manuscript is available in PDF format.

Supporting Materials