Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models

Bernoulli

Volumn 14, Issue 1, 2008, Pages 155-179

  Olsson, Jimmy ^a   Cappé, Olivier ^a   Douc, Randal ^b   Moulines, acEric ^a  

^a TELECOM PARISTECH   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

EM algorithm; Exponential family; Particle filters; Sequential Monte Carlo methods; State space models; Stochastic volatility model

Indexed keywords

EID: 41449089271     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/07-BEJ6150     Document Type: Article

References (15)

1. Andrieu, C. and Doucet, A. (2003). Online expectation-maximization type algorithms for parameter estimation in general state space models. In Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. 6 V169-V172.
2. Cappé, O., Moulines, E. and Rydén, T. (2005). Inference in Hidden Markov Models. New York: Springer.
3. Del Moral, P. (2004). Feynman-Kac Formulae. Genealogical and Interacting Particle Systems with Applications. New York: Springer.
4. Del Moral, P. and Doucet, A. (2003). On a class of genealogical and interacting Metropolis models. Séminaire de Probabilités XXXVII (J. Azéma, M. Emery, M. Ledoux and M. Yor, eds.). Lecture Notes in Math. 1832 415-446. Berlin: Springer.
5. Douc, R., Fort, G., Moulines, E. and Priouret, P. (2007). Forgetting of the initial distribution for hidden Markov models. Available at http:// arxiv.org/abs/math/0703836.
6. Doucet, A., de Freitas, N. and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice. New York: Springer.
7. Doucet, A., Godsill, J. and West, M. (2004). Monte Carlo smoothing for nonlinear time series. J. Amer. Statist. Assoc. 99 156-168.
8. Fort, G. and Moulines, É. (2003). Convergence of the Monte Carlo expectation maximization for curved exponential families. Ann. Statist. 31 1220-1259.
9. Hull, J. and White, A. (1987). The pricing of options on assets with stochastic volatilities. J. Finance 42 281-300.
10. Jaquier, E., Polson, N.G. and Rossi, P.E. (1994). Bayesian analysis of stochastic volatility models (with discussion). J. Bus. Econom. Statist. 12 371-417.
11. Kitagawa, G. and Sato, S. (2001). Monte Carlo smoothing and self-organising state-space model. In Sequential Monte Carlo Methods in Practice (A. Doucet, N. de Freitas and N. Gordon, eds.) 178-195. New York: Springer.
12. Kleptsyna, M.L. and Veretennikov, A.Y. (2007). On discrete time ergodic filters with wrong initial conditions. Technical report, Univ. Main and Univ. Leeds.
13. Pitt, M. K. and Shephard, N. (1999). Filtering via simulation: Auxiliary particle filters. J. Amer. Statist. Assoc. 94 590-599.
14. Ristic, B., Arulampalam, M. and Gordon, A. (2004). Beyond the Kalman Filter: Particle Filters for Target Tracking. Atrech House Radar Library.
15. Wei, G.C.G. and Tanner, M.A. (1991). A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J. Amer. Statist. Assoc. 85 699-704.