References for State Space Models and Filtering

State Space Models and Monte Carlo Filtering : Major References

State Space Models

Kalman filter and related filtering/smoothing techniques

Anderson, B.D.O. and Moore, J.B. (1979). Optimal Filtering, Prentice-Hall.

Ansley, C.F. and Kohn, R. (1985), Estimation, filtering and smoothing in state space models with incompletely specified initial conditions, Annals of Statistics, 13, 1286-1316.

de Jong, P. (1989). Smoothing and interpolation with the state space model, J. American Statistical Association, 85, 1085-1088.

de Jong, P. (1991). The diffuse Kalman filter, Annals of Statistics, 19, 1073-83.

Durbin J. and Koopman S.J. (2001). Time Series Analysis by State Space Methods, Oxford University Press.

Harvey, A.C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, London.

Jones, R.H. (1993). Longitudinal Data with Serial Correlation: A State Space Approach. Chapman&Hall, London.

Kalman, R.E. (1960). A new approach to linear filtering and prediction theory, Journal of Basic Engineering, Transactions ASME, Series D, 82, 35-45.

Koopman, S.J. (1993). Disturbance smoother for state space models, Biometrika, 80, 117-126.

Maximum likelihood estimation of parameters and inference

de Jong, P. (1988). The likelihood for a state space model, Biometrika, 75, 165-169.

Engle, R.F. and Watson, M.W., (1981). A one factor multivariate time series models of metropolitan wage rates, Journal of American Statistical Association, 76, 774-781.

Jensen J.L., Petersen, N.V., (1999). Asymptotic normality of the maximum likelihood estimator in state space models, Annals of Statistics, 27, 514-535.

Shephard, N. and Pitt, M.K. (1997). Likelihood analysis of non-Gaussian measurement time series, Biometrika, 84, 653-667.

Schweppe, F. (1965). Evaluation of likelihood functions for Gaussian signals, IEEE Transactions on Information Theory, 11, 61-70.

Watson, M.W. and Engle, R.F. (1983). Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models, Journal of Econometrics, 23, 385-400.

Monte Carlo approaches for state space models

Arnaud, D., Nando De, F., and Neil, G. (2001). Sequential Monte Carlo Methods in Practice. Springer.

Carlin, B.P., Polson, N.G., and Stoffer, D.S. (1992). A Monte Carlo approach to nonnormal and nonlinear state-space modeling, Journal of American Statistical Association, 87, 493-500

Carter, C.K. and Kohn R. (1994). On Gibbs sampling for state space models, Biometrika, 81, 541-553.

Carter, C.K. and Kohn R. (1996). Markov chain Monte Carlo in conditionally Gaussian state space models, Biometrika, 83, 589-601.

Chen R. and Liu J. (2000). Mixture Kalman Filters, J. of Royal Statistical Society, Series B, 62, 493-508.

de Jong, P. and Shephard, N. (1995). The simulation smoother for time series models, Biometrika, 82, 339-350.

Durbin, J. and Koopman, S.J. (2000). Time series analysis for non-Gaussian observations based on state space models from both classical and Bayesian perspectives (with discussion), J. Royal Statistical Society, Series B, 62, 3-56.

Gilks, W.R. and Berzuini, C. (2001). Following a moving target – Monte Carlo inference for dynamic Bayesian models, J. Royal Statistical Society, Series B, 63, 127-146.

Kitagawa, G. (1989). Non-Gaussian state space modeling for non-stationary time series (with discussion), J. of American Statistical Association, 82, 1032-1063.

Kitagawa, G. (1996). Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics, 5, 1-25.

Liu, J.S. and Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems, Journal of the American Statistical Association, 93, 1032-1044.

West, M. and Harrison, J. (1999). Bayesian Forecasting and Dynamic models, 2nd edition, New York, Springer.

Related books on Monte Carlo techniques

Arnaud, D., Nando De, F., and Neil, G. (2001). Sequential Monte Carlo Methods in Practice. Springer-Verlag.

Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1996). Markov Chain Monte Carlo in Practice, Chapman&Hall, London.

Liu, J.S. (2001). Monte Carlo Strategies in Scientific Computing, Springer-Verlag, New York.

Robert C.P. and Casella G. (1999), Monte Carlo Statistical Methods, Springer-Verlag, New York.

Particle Filter

Arnaud, D., Nando De, F., and Neil, G. (editors, 2001). Sequential Monte Carlo Methods in Practice. Springer.

Kitagawa, G. (1996). Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics. 5(1): 1-25.

Kitagawa, G. (1998). Self-organizing state space model. Journal of the American Statistical Association. 93, 1203-1215.

Liu, J. and West, W. (2001). Combined Parameter and State Estimation in Simulation-Based Filtering. Sequential Monte Carlo Methods in Practice. Arnaud, D. et al. (ed., 2001). Pp. 197-224.

Liu, J.S. and Chen, R. (1995). Blind deconvolution via sequential imputations. Journal of the American Statistical Association. 90, 567-576.

Liu, J.S. and Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association. 93, 1032-1044.

Liu, J.S., Chen, R. and Logvinenko, T. (2001). A Theoretical Framework for Sequential Importance Sampling with Resampling. Sequential Monte Carlo Methods in Practice. Arnaud, D. et al. (ed., 2001). Pp. 225-246.

Pitt, M.K., and Shephard, N. (1999). Filtering via Simulation: Auxiliary Particle Filters. Journal of the American Statistical Association. 94, 590-599.

Stavropoulos, P. and Titterington, D.M. (2001). Improved Particle Filters and Smoothing. Sequential Monte Carlo Methods in Practice. Arnaud, D. et al. (ed., 2001). Pp. 295-318.

Wecker, W.E., and Ansley, C. F. (1983). The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing. Journal of the American Statistical Association, 78, 81-89.

West, M. (1993). Mixture models, Monte Carlo, Bayesian updating and dynamic models, in J.H. Newton(editor), Computing Science and Statistics: Proceedings of the 24th Symposium on the Interface, Interface Foundation of North America, Fairfax Station, Virginia, pp. 325-333.

Introductory References for Students and New Researchers

Books Related to State Space Models and Particle Filter

Durbin J. and Koopman S.J. (2001). Time Series Analysis by State Space Methods, Oxford University Press.

Arnaud, D., Nando De, F., and Neil, G. (editors, 2001). Sequential Monte Carlo Methods in Practice. Springer.

Harvey, A.C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge, Cambridge University Press.

Anderson, B.D.O. and Moore, J.B. (1979). Optimal Filtering, Prentice-Hall.

Books on Monte Carlo Methods

Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1996). Markov Chain Monte Carlo in Practice, Chapman&Hall, London.

Liu, J.S. (2001). Monte Carlo Strategies in Scientific Computing, Springer-Verlag, New York.