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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)

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    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

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    File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp651.pdf
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    Bibliographic Info

    Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 651.

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    Length: 44 pages
    Date of creation: 2002
    Date of revision:
    Handle: RePEc:wrk:warwec:651

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    References

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    1. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
    2. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
    3. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers 205, Board of Governors of the Federal Reserve System (U.S.).
    4. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
    5. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    6. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
    7. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    8. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    9. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    10. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
    11. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
    12. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    13. Christophe Andrieu & Arnaud Doucet, 2002. "Particle filtering for partially observed Gaussian state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 827-836.
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    Cited by:
    1. 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.
    2. Giuliano De Rossi, 2010. "Maximum Likelihood Estimation of the Cox–Ingersoll–Ross Model Using Particle Filters," Computational Economics, Society for Computational Economics, vol. 36(1), pages 1-16, June.
    3. David N. DeJong & Hariharan Dharmarajan & Roman Liesenfeld & Guilherme Moura & Jean-Francois Richard, 2007. "Efficient Likelihood Evaluation in State-Space Representations," Working Papers 374, University of Pittsburgh, Department of Economics, revised Dec 2008.
    4. 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.
    5. 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.
    6. 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.

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