NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH
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Tempered Particle Filtering

Edward Herbst, Frank Schorfheide

NBER Working Paper No. 23448
Issued in May 2017
NBER Program(s):Economic Fluctuations and Growth, Monetary Economics

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.

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Document Object Identifier (DOI): 10.3386/w23448

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