Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models

Journal of Computational and Graphical Statistics

Volumn 5, Issue 1, 1996, Pages 1-25

  Reini, Mauro ^a  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

Fixed interval smoothing; Non Gaussian state space model; Nonstationary time series; Recursive filtering; Time series modeling

Indexed keywords

EID: 0030304310     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.1996.10474692     Document Type: Article

References (27)

1. Akaike, H. (1973), “Information Theory and an Extension of the Maximum Likelihood Principle,” in Second International Symposium on Information Theory, eds. B. N. Petrov and F. Csaki, Budapest: Akademiai Kiado, pp. 267-281.
2. Alspach, D. L., and Sorenson, H. W. (1972), “Nonlinear Bayesian Estimation Using Gaussian Sum Approximations,” IEEE Transactions on Automatic Control, AC-17, 439-448.
3. Anderson, B. D. O., and Moore, J. B. (1979), Optimal Filtering, Englewood Cliffs, NJ: Prentice-Hall.
4. Andrede Netto, M. L., Gimeno, L., and Mendes, M. J. (1978), “On the Optimal and Suboptimal Nonlinear Filtering Problem for Discrete-Time Systems,” IEEE Transactions on Automatic Control, 23, 1062-1067.
5. Carlin, B.P., Poison, N.G., and Stoffer, D.S. (1992), “A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling,” Journal of the American Statistical Association, 87, 439-500.
6. Fahrmeir, L. (1992), “Posterior Mode Estimation by Extended Kalman Filtering for Multivariate Dynamic Generalized Linear Models,” Journal of the American Statistical Association, 87, 501-509.
7. Fahrmeir, L., and Kaufmann, H. (1991), “On Kalman Filtering, Posterior Mode Estimation and Fisher Scoring in Dynamic Exponential Family Regression,” Metrika, 38, 37-60.
8. Friihwirth-Schnatter, S. (1994), “Data Augmentation and Dynamic Linear Models,” Journal of Time Series Analysis, 15, 183-202.
9. Harrison, P. J., and Stevens, C. F. (1976), “Bayesian Forecasting” (with discussion), Journal of the Royal Statistical Society, Ser. B, 34, 1—41.
10. Harvey, A. (1989), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge, UK: Cambridge University Press.
11. Hodges, P. E., and Hale, D. F. (1993), “A Computational Method for Estimating Densities of non-Gaussian Nonstationary Univariate Time Series,” Journal of Time Series Analysis, 14, 163-178.
12. Kitagawa, G. (1987), “Non-Gaussian State-Space Modeling of Nonstationary Time Series” (with discussion), Journal of the American Statistical Association, 82, 1032—1063.
13. Kitagawa, G. (1989), “Non-Gaussian Seasonal Adjustment,” Computers & Mathematics with Applications, 18, 503-514.
14. Kitagawa, G. (1991), “A Nonlinear Smoothing Method for Time Series Analysis,” Statistica Sinica, 1, 371-388.
15. Kitagawa, G. (1993), “A Monte Carlo Filtering and Smoothing Method for Non-Gaussian Nonlinear State Space Models,” Proceedings of the 2nd V.S.-Japan Joint Seminar on Statistical Time Series Analysis, pp. 110-131.
16. Kitagawa, G. (1994), “The Two-Filter Formula for Smoothing and an Implementation of the Gaussian-Sum Smoother,” Annals of the Institute of Statistical Mathematics, 46, 605-623.
17. Kitagawa, G., and Gersch, W. (1984), “A Smoothness Priors-State Space Modeling of Time Series With Trend and Seasonality,’ Journal of the American Statistical Association, 79, 378-389.
18. Masreliez, C. J. (1975), “Approximate Non-Gaussian Filtering With Linear State and Observation Relations,” IEEE Transactions on Automatic Control, AC-20, 107-110.
19. Meinhold, R. J., and Singpurwalla, N. D. (1989), “Robustification of Kalman Filter Models,” Journal of the American Statistical Association, 84, 479-486.
20. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992), Numerical Recipes in FORTRAN, The Art of Scientific Computing, (2nd ed.), Cambridge, UK: Cambridge University Press.
21. Sage, A. P., and Melsa, J. L. (1971), Estimation Theory with Application to Communication and Control, New York: McGraw-Hill.
22. Sakamoto, Y., Ishiguro, M., and Kitagawa, G (1986), Akaike Information Criterion Statistics, Tokyo: D. Reidel.
23. Schnatter, S. (1992), “Integration-Based Kalman-Filtering for a Dynamic Generalized Linear Trend Model,” Computational Statistics and Data Analysis, 13, 447-459.
24. Smith, R. L., and Miller, J. E. (1986), “A Non-Gaussian State Space Model and Application to Prediction of Records,” Journal of the Royal Statistical Society, Ser. B, 48, 79-88.
25. Tanizaki, H. (1993), “Nonlinear Filters,” Lecture Notes in Economics and Mathematical Systems, No. 400, New York: Springer-Verlag.
26. Tong, H. (1977), “Some Comments on the Canadian Lynx Data,” Journal of the Royal Statistical Society, A-140, 432-436.
27. West, M., Harrison, P.J., and Migon, H. S. (1985), “Dynamic Generalized Linear Models and Bayesian Forecasting” (with discussion), Journal of the American Statistical Association, 80, 73-97.