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Smooth Particle Filters for Likelihood Evaluation and Maximisation

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  • Pitt, Michael K

    (Department of Economics, University of Warwick)

Abstract

In this paper, a method is introduced for approximating the likelihood for the unknown parameters of a state space model. The approximation converges to the true likelihood as the simulation size goes to infinity. In addition, the approximating likelihood is continuous as a function of the unknown parameters under rather general conditions. The approach advocated is fast, robust and avoids many of the pitfalls associated with current techniques based upon importance sampling. We assess the performance of the method by considering a linear state space model, comparing the results with the Kalman filter, which delivers the true likelihood. We also apply the method to a non-Gaussian state space model, the Stochastic Volatility model, finding that the approach is efficient and effective. Applications to continuous time finance models are also considered. A result is established which allows the likelihood to be estimated quickly and efficiently using the output from the general auxilary particle filter. keywords: Importance Sampling ; Filtering ; Particle filter ; Simulation ; SIR ; State space

Suggested Citation

  • Pitt, Michael K, 2002. "Smooth Particle Filters for Likelihood Evaluation and Maximisation," The Warwick Economics Research Paper Series (TWERPS) 651, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:651
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp651.pdf
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    References listed on IDEAS

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    Cited by:

    1. A. Hannart & A. Carrassi & M. Bocquet & M. Ghil & P. Naveau & M. Pulido & J. Ruiz & P. Tandeo, 2016. "DADA: data assimilation for the detection and attribution of weather and climate-related events," Climatic Change, Springer, vol. 136(2), pages 155-174, May.
    2. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    3. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
    4. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    5. Creal, D., 2009. "A survey of sequential Monte Carlo methods for economics and finance," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    6. Davide Raggi & Silvano Bordignon, 2011. "Volatility, Jumps, and Predictability of Returns: A Sequential Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 30(6), pages 669-695.
    7. Ralph S.J. Koijen & Jules H. van Binsbergen & Juan F. Rubio-Ramírez & Jesus Fernandez-Villaverde, 2008. "Likelihood Estimation of DSGE Models with Epstein-Zin Preferences," 2008 Meeting Papers 1099, Society for Economic Dynamics.
    8. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
    9. Kau, James B. & Keenan, Donald C. & Lyubimov, Constantine & Carlos Slawson, V., 2011. "Subprime mortgage default," Journal of Urban Economics, Elsevier, vol. 70(2-3), pages 75-87, September.
    10. Huang, Shirley J. & Yu, Jun, 2010. "Bayesian analysis of structural credit risk models with microstructure noises," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2259-2272, November.
    11. Roman Liesenfeld & Guilherme V. Moura & Jean-François Richard & Hariharan Dharmarajan, 2013. "Efficient Likelihood Evaluation of State-Space Representations," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 538-567.
    12. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    13. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    14. Benedikt Rotermann & Bernd Wilfling, 2015. "Estimating rational stock-market bubbles with sequential Monte Carlo methods," CQE Working Papers 4015, Center for Quantitative Economics (CQE), University of Muenster.
    15. Nicholas G. Polson & Jonathan R. Stroud & Peter Müller, 2008. "Practical filtering with sequential parameter learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 413-428.
    16. Duan, Jin-Chuan & Fulop, Andras, 2009. "Estimating the structural credit risk model when equity prices are contaminated by trading noises," Journal of Econometrics, Elsevier, vol. 150(2), pages 288-296, June.
    17. Kleppe, Tore Selland & Skaug, Hans Julius, 2012. "Fitting general stochastic volatility models using Laplace accelerated sequential importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3105-3119.
    18. repec:wyi:journl:002113 is not listed on IDEAS
    19. Michael S. Johannes & Nicholas G. Polson & Jonathan R. Stroud, 2009. "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2559-2599, July.
    20. repec:wyi:journl:002173 is not listed on IDEAS

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