Abstract
We review Kalman filter and related smoothing methods for the latent trajectory in multivariate time series. The latent effects in the model are modelled as vector unobserved components for which we assume particular dynamic stochastic processes. The parameters in the resulting multivariate unobserved components time series models will be estimated by maximum likelihood methods. Some essential details of the state space methodology are discussed in this chapter. An application in the modelling of traffic safety data is presented to illustrate the methodology in practice.
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References
Box, G. E. P., & Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. Journal of the American Statistical Association, 70, 70-79.
Commandeur, J. J. F., & Koopman, S. J. (2007). An Introduction to State Space Time Series Analysis. Oxford: Oxford University Press.
Durbin, J., & Koopman, S. J. (2001). Time Series Analysis by State Space Methods. Oxford: Oxford University Press.
Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge: Cambridge University Press.
Harvey, A. C., & J. Durbin (1986). The effects of seat belt legislation on British road casualties: A case study in structural time series modelling. Journal of the Royal Statistical Society A, 149 (3), 187-227.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal Basic Engineering, Transactions ASMA Series D, 82, 35-45.
Koopman, S. J., Harvey, A. C., Doornik, J. A., & Shephard, N. (2007). Stamp 8.0: Structural Time Series Analyser, Modeller and Predictor. London: Timberlake Consultants.
Nocedal, J., & Wright, S. J. (1999). Numerical Optimization. New York: Springer Verlag.
Shumway, R. H., & Stoffer, D. S. (1982). An approach to time series smoothing and forecasting using the EM algorithm. Journal of Time Series Analysis, 3, 253-264.
Watson, M. W., & Engle, R. F. (1983). Alternative algorithms for the estimation of dynamic factor, MIMIC and varying coefficient regression. Journal of Econometrics, 23, 385-400.
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Commandeur, J.J.F., Koopman, S.J., van Montfort, K. (2010). State Space Methods for Latent Trajectory and Parameter Estimation by Maximum Likelihood. In: van Montfort, K., Oud, J., Satorra, A. (eds) Longitudinal Research with Latent Variables. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11760-2_6
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DOI: https://doi.org/10.1007/978-3-642-11760-2_6
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