A Particle-Kalman Double Filtering Method for State Space Models with Superposed Latent States

Abstract

We address the inefficiency of particle filters in nonlinear and non-Gaussian state space models with superposed latent states, such as multi-component stochastic volatility and intensity models. Exploiting the superposition structure, we propose a simple two-step method: apply a particle filter to the superposed state, then recover individual components via a Kalman filter. This double filtering approach reduces the effective state dimension that can lead to particle degeneracy, and allows for likelihood-based inference. Simulation results show substantial gains in efficiency over particle filters that use the optimal proposal density but do not exploit the superposition. We apply the method to study different components in the common idiosyncratic volatility of stock returns and explore their pricing implications.