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.
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|Date of creation:||May 2017|
|Contact details of provider:|| Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.|
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- Robert Kollmann, 2015.
"Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning,"
Springer;Society for Computational Economics, vol. 45(2), pages 239-260, February.
- Robert Kollmann, 2014. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning," ULB Institutional Repository 2013/250061, ULB -- Universite Libre de Bruxelles.
- Bognanni, Mark & Herbst, Edward, 2014.
"Estimating (Markov-Switching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach,"
1427, Federal Reserve Bank of Cleveland.
- Bognanni, Mark & Herbst, Edward, 2015. "Estimating (Markov-Switching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach," Finance and Economics Discussion Series 2015-116, Board of Governors of the Federal Reserve System (U.S.).
- Nicolas Chopin, 2002.
"A sequential particle filter method for static models,"
Biometrika Trust, vol. 89(3), pages 539-552, August.
- Nicolas Chopin, 2000. "A Sequential Particle Filter Method for Static Models," Working Papers 2000-45, Center for Research in Economics and Statistics.
- Ajay Jasra & David A. Stephens & Arnaud Doucet & Theodoros Tsagaris, 2011. "Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 1-22, March. Full references (including those not matched with items on IDEAS)
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