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Tempered particle filtering

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  • Herbst, Edward
  • Schorfheide, Frank

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 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.

Suggested Citation

  • Herbst, Edward & Schorfheide, Frank, 2019. "Tempered particle filtering," Journal of Econometrics, Elsevier, vol. 210(1), pages 26-44.
    • Handle: RePEc:eee:econom:v:210:y:2019:i:1:p:26-44
    DOI: 10.1016/j.jeconom.2018.11.003
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    2. Pablo Cuba‐Borda & Luca Guerrieri & Matteo Iacoviello & Molin Zhong, 2019. "Likelihood evaluation of models with occasionally binding constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1073-1085, November.
    3. Wolf, Elias, 2022. "Estimating growth at risk with skewed stochastic volatility models," Discussion Papers 2022/2, Free University Berlin, School of Business & Economics.
    4. Herbst, Edward & Schorfheide, Frank, 2019. "Tempered particle filtering," Journal of Econometrics, Elsevier, vol. 210(1), pages 26-44.
    5. Sergei Seleznev, 2016. "Solving DSGE models with stochastic trends," Bank of Russia Working Paper Series wps15, Bank of Russia.
    6. Boehl, Gregor & Strobel, Felix, 2024. "Estimation of DSGE models with the effective lower bound," Journal of Economic Dynamics and Control, Elsevier, vol. 158(C).
    7. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    8. Wolf, Elias, 2023. "Estimating Growth at Risk with Skewed Stochastic Volatility Models," VfS Annual Conference 2023 (Regensburg): Growth and the "sociale Frage" 277696, Verein für Socialpolitik / German Economic Association.
    9. Umberto Picchini & Adeline Samson, 2018. "Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models," Computational Statistics, Springer, vol. 33(1), pages 179-212, March.
    10. Montes-Galdón, Carlos & Paredes, Joan & Wolf, Elias, 2022. "Conditional density forecasting: a tempered importance sampling approach," Working Paper Series 2754, European Central Bank.
    11. Minsu Chang, 2019. "A House Without a Ring: The Role of Changing Marital Transitions for Housing Decisions," 2019 Meeting Papers 514, Society for Economic Dynamics.
    12. Sanha Noh, 2020. "Posterior Inference on Parameters in a Nonlinear DSGE Model via Gaussian-Based Filters," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 795-841, December.
    13. Andras Fulop & Jeremy Heng & Junye Li, 2022. "Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models," Papers 2201.01094, arXiv.org.

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    More about this item

    Keywords

    Bayesian analysis; DSGE models; Nonlinear filtering; Monte Carlo methods;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General

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