Working Paper: NBER ID: w23448
Authors: Edward Herbst; Frank Schorfheide
Abstract: The accuracy of particle filters for nonlinear state-space models crucially depends on the proposal distribution that mutates time t-1 particle values into time t values. In the widely-used bootstrap particle filter, this distribution is generated by the state-transition equation. While straightforward to implement, the practical performance is often poor. We develop a self-tuning particle filter in which the proposal distribution is constructed adaptively through a sequence of Monte Carlo steps. Intuitively, we start from a measurement error distribution with an inflated variance, and then gradually reduce the variance to its nominal level in a sequence of tempering steps. We show that the filter generates an unbiased and consistent approximation of the likelihood function. Holding the run time fixed, our filter is substantially more accurate in two DSGE model applications than the bootstrap particle filter.
Keywords: Particle Filtering; Dynamic Stochastic General Equilibrium; Likelihood Approximation
JEL Codes: C11; C32; E32
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| tempered particle filter (C53) | more accurate approximation of the likelihood function (C51) |
| bootstrap particle filter (C46) | less accurate approximation of the likelihood function (C51) |
| tempered particle filter (C53) | reduces Monte Carlo error relative to the bootstrap particle filter (C53) |
| tempered particle filter (C53) | improves accuracy of particle weights (C46) |