Abstract
In some state espace models for time series, the error terms have singular multinormal distribution. In this paper the mathematical deduction of the Kalman Filter for these models is presented.
References
Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis, John Wiley and Sons, Inc, New York.
Anderson, D. O. and Moore, J. B. (1979). Optimal Filtering, Prentice-Hall, Inc., New Jersey (U. S. A.).
Aoki, M. (1990). State Space Modeling of Time Series, Springer-Verlag, Berlin.
Catlin, D. (1989). Estimation, Control and the discrete Kalman Filter, Springer-Verlag, Berlin.
Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge.
Kohn, R. and Ansley, C. F. (1983). Fixed interval estimation in state space models when some of the data are missing or aggregated, Biometrika, Vol. 70, 3, pp 683–8.
Mardia, K. V., Kent, J. J. and Bibby, J. M. (1979). Multivariate Analysis, Academic Press, Inc., London.
Marsaglia, G. (1964). Conditional Means and Covariances of Normal Variables with Singular Covariance Matrix, Journal of the American Statistical Association, 59, pp. 1203–1204.
Meinhold, R. J. and Singpurwalla, N. D. (1983). Understanding the Kalman Filter, The American Statistician, Vol. 37, Nº2.
West, M. and Harrison, P. J. (1989). Bayesian Forecasting and Dynamic Models, Springer-Verlag, Berlin.

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