Tempered Particle Filtering

67 Pages Posted: 27 Oct 2016

See all articles by Edward Herbst

Edward Herbst

Board of Governors of the Federal Reserve System

Frank Schorfheide

University of Pennsylvania - Department of Economics; Centre for Economic Policy Research (CEPR)

Multiple version iconThere are 3 versions of this paper

Date Written: October 25, 2016

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 steps that we call tempering. 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: Bayesian Analysis, DSGE Models, Nonlinear Filtering, Monte Carlo Methods

JEL Classification: C11, C15, E10

Suggested Citation

Herbst, Edward and Schorfheide, Frank, Tempered Particle Filtering (October 25, 2016). PIER Working Paper No. 16-017. Available at SSRN: https://ssrn.com/abstract=2858991 or http://dx.doi.org/10.2139/ssrn.2858991

Edward Herbst

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Frank Schorfheide (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

HOME PAGE: http://www.econ.upenn.edu/~schorf

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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