Bandwidth Selection in Pre-Smoothed Particle Filters

Abstract

This paper introduces the Pre-Smoothed Particle Filter (PSPF) as a regularized alternative to the Sampling Importance Resampling (SIR) filter for non-linear state space models with additive Gaussian observation noise. The PSPF adaptively bridges the unbiased, but variance-prone, SIR filter and the biased, but less variance-prone Gaussian update filter. Our main contribution is the adaptive determination of the degree of smoothing in each time step. We illustrate the approach using examples from econometrics, namely a continuous time short term interest rate model and a dynamic stochastic general equilibrium model fitted to noisy data. The PSPF is shown to be highly suited for dynamic models with high signal-to-noise ratio, for which the SIR filter has problems.