Abstract
By the progress of fast computing facilities and various computing technologies, it becomes realistic to apply computer intensive methods to statistical analysis. In time series analysis, sequential Monte Carlo methods was developed for general state space models which enables to consider very complex nonlinear non-Gaussian models.
In this paper, we show algorithms, implementations and parameter estimation for Monte Carlo filter and smoother. Various ways of the use of parallel computer are also discussed. The usefulness of the general state space modeling is illustrated with several examples.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alspach, D. L., and Sorenson, H. W., (1972). Nonlinear Bayesian Estimation Using Gaussian Sum Approximations. IEEE Transactions on Automatic Control, AC-17, 439–448.
Anderson, B. D. O., and Moore, J. B., (1979). Optimal Filtering. Prentice-Hall, New Jersey.
Andrede Netto, M. L., Gimeno, L. and Mendes, M. J., (1978). On the optimal and suboptimal nonlinear filtering problem for discrete-time systems, IEEE Trans. Automat. Control, 23, 1062–1067.
Doucet, A., de Freitas, N. and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice. Springer-Verlag, New York.
Gordon, N. J., Salmond, D. J. and Smith, A. F. M., (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proceedings-F, 140, 107–113.
Harrison, P.J. and Stevens, C.F. (1976). Bayesian Forcasting, Journal of the Royal Statistical Society, Series B, 38, 205–247.
Harvey, A.C. (1989). Forecasting structural time series models and the Kalman filter, Cambbridge University Press, Victoria, Australia.
Higuchi, T. (1997). Monte Carlo filter using the Genetic algorithm operators, Journal of Statistical Computation and Simulation, 59, 1–23.
Higuchi, T. (2001). Evolutionary Time Series Model with Parallel Computing, Proceedings of the 3rd Japan-US Joint Seminar on Statistical Time Series Analysis, Kyoto, Japan, June 18–22, 2001, 183–190.
Kitagawa, G., (1987). Non-Gaussian state-space modeling of nonstationary time series (with discussion), Journal-of the American Statistical Association, 82, 1032–1063.
Kitagawa, G., (1991). A nonlinear smoothing method for time series analysis, Statistica Sinica, 1, 371–388.
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.
Kitagawa, G., (1996). Monte Carlo filter and smoother for non-Gaussian nonlinear state space model, Journal of Computational and Graphical Statistics, 5, 1–25.
Kitagawa, G., (1998). Self-Organizing State Space Model, Journal of the American Statistical Association, 93, 1203–1215.
Kitagawa, G. and Gersch, W., (1996). Smoothness Priors Analysis of Time Series, Springer-Verlag, New York.
Ljung, L., (1979). Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems, IEEE Transactions on Automatic Control, AC-24, 36–50.
Solo, V., (1980). Some aspect of recursive parameter estimation, International Journal of Control, 32, 395–410.
Takahashi, A. and Sato, S. (2001). A Monte Carlo filtering approach for estimating the term structure of interest rates, Annals of the Institute of Statistical Mathematics, 53, 50–62.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kitagawa, G., Higuchi, T., Sato, S. (2002). Computational Methods for Time Series Analysis. In: Härdle, W., Rönz, B. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57489-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-57489-4_2
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1517-7
Online ISBN: 978-3-642-57489-4
eBook Packages: Springer Book Archive