Smooth Particle Filters for Likelihood Evaluation and Maximisation
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
|Date of creation:||2002|
|Date of revision:|
|Contact details of provider:|| Postal: CV4 7AL COVENTRY|
Phone: +44 (0) 2476 523202
Fax: +44 (0) 2476 523032
Web page: http://www2.warwick.ac.uk/fac/soc/economics/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ghysels, E. & Harvey, A. & Renault, E., 1995.
95.400, Toulouse - GREMAQ.
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
- Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard & Michael K Pitt, 1995.
"Likelihood analysis of non-Gaussian parameter driven models,"
15 & 108., Economics Group, Nuffield College, University of Oxford.
- Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
- 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.
- 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.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- 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.
- 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.
- 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.
- Diebold, Francis X & Nerlove, Marc, 1989.
"The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
- 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.).
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
When requesting a correction, please mention this item's handle: RePEc:wrk:warwec:651. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Margaret Nash)
If references are entirely missing, you can add them using this form.