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Smooth particle filters for likelihood evaluation and maximisation

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  • Pitt, Michael K.

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.

Suggested Citation

  • Pitt, Michael K., 2002. "Smooth particle filters for likelihood evaluation and maximisation," Economic Research Papers 269464, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:269464
    DOI: 10.22004/ag.econ.269464
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    Cited by:

    1. Anastasis Kratsios & Cody B. Hyndman, 2017. "Non-Euclidean Conditional Expectation and Filtering," Papers 1710.05829, arXiv.org, revised Sep 2018.
    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. Tarjáni, Hajnalka & Csorba, Gergely, 2005. "Nyári Műhely. MTA Közgazdaságtudományi Intézet, Budapest, 2005. június 27-29 [Summer workshop]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(9), pages 698-706.
    4. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    5. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    6. Xinglin Yang, 2018. "Good jump, bad jump, and option valuation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(9), pages 1097-1125, September.
    7. Giuliano De Rossi, 2010. "Maximum Likelihood Estimation of the Cox–Ingersoll–Ross Model Using Particle Filters," Computational Economics, Springer;Society for Computational Economics, vol. 36(1), pages 1-16, June.
    8. Maciej Augustyniak & Mathieu Boudreault & Manuel Morales, 2018. "Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 165-188, March.
    9. 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, June.
    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. Elena Ehrlich & Ajay Jasra & Nikolas Kantas, 2015. "Gradient Free Parameter Estimation for Hidden Markov Models with Intractable Likelihoods," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 315-349, June.
    12. 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.
    13. Giuliano De Rossi, 2004. "Maximum likelihood estimation of the Cox-Ingersoll-Ross model using particle filters," Computing in Economics and Finance 2004 302, Society for Computational 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. Karamé, Frédéric, 2018. "A new particle filtering approach to estimate stochastic volatility models with Markov-switching," Econometrics and Statistics, Elsevier, vol. 8(C), pages 204-230.
    16. 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, April.
    17. 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.
    18. 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.

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