Tempered Particle Filtering
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.
Schorfheide gratefully acknowledges financial support from the National Science Foundation under the grant SES 1424843. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research, the Board of Governors, or the Federal Reserve System.