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Tempered Particle Filtering

Listed author(s):
  • Edward Herbst
  • Frank Schorfheide

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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File URL: http://www.nber.org/papers/w23448.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 23448.

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Date of creation: May 2017
Handle: RePEc:nbr:nberwo:23448
Note: EFG ME
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  1. Robert Kollmann, 2015. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 239-260, February.
  2. Bognanni, Mark & Herbst, Edward, 2014. "Estimating (Markov-Switching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach," Working Paper 1427, Federal Reserve Bank of Cleveland.
  3. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
  4. 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.
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