Particle rejuvenation of Rao-Blackwellized Sequential Monte Carlo smoothers for Conditionally Linear and Gaussian models

TL;DR

This paper introduces particle rejuvenation steps in Rao-Blackwellized Sequential Monte Carlo smoothers for conditionally linear Gaussian models, improving sampling diversity and accuracy in smoothing distributions.

Contribution

It proposes a novel particle rejuvenation approach for Rao-Blackwellized smoothers, enhancing the sampling of regimes and reducing variance in smoothing estimates.

Findings

Improved smoothing accuracy with rejuvenation steps.

Enhanced sampling diversity in regime sequences.

Application to crude oil market data demonstrates effectiveness.

Abstract

This paper focuses on Sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of regimes and observations, using variants of the Kalman filter / smoother. The first successful attempt to use Rao-Blackwellization for smoothing extends the Bryson-Frazier smoother for Gaussian linear state space models using the generalized two-filter formula together with Kalman filters / smoothers. More recently, a forward backward decomposition of smoothing distributions mimicking the Rauch-Tung-Striebel smoother for the regimes combined with backward Kalman updates has been introduced. This paper investigates the benefit of introducing additional rejuvenation steps in all these algorithms to sample at each time instant new regimes conditional on the forward and backward particles. This defines particle based approximations of the smoothing distributions whose support is not restricted to the set of particles sampled in the forward or backward filter. These procedures are applied to commodity markets which are described using a two factor model based on the spot price and a convenience yield for crude oil data.