Aniello Fedullo


The Kalman filter is the celebrated algorithm giving a recursive solution of the prediction problem for time series. After a quite general formulation of the prediction problem, the contributions of its solution by the great mathematicians Kolmogorov and Wiener are shorthly recalled and it is showed as Kalman filter furnishes the optimal predictor, in the sense of least squares, for processes which satisfy the linear models with a finite number of parameters, that are the ARMA models.

Full Text:



Box G.E.P. e G.M. Jenkins (1970), Time series Analysis, Forecasting and Control, Holden-Day, San Francisco.

Caines P.E. (1972), Relationship between Box-Kenkins-Astrom control and Kalman linear regulator, Proc. IEEE, 119, 615--620.

Kalman R.E. (1960), A new approach to linear filtering and prediction problems, Trans. ASME J. Basic Engrg., ser. D, 82, 35--45.

Kalman R.E. e R.S. Bucy (1961), New results in linear filtering and prediction problems, Trans. ASME J. Basic Engrg., ser. D, 83, 95--108.

Kolmogoroff A.N. (1941), Interpolation und extrapolation von stationaren Zufallingen Folgen, Bull. Acad. Sci. (Nauk), U.S.S.R., ser. math., 5, 3--14.

Papoulis A. (1965), Probability, random variables and stochastic processes, Mc Graw Hill, New York.

Wiener N. (1949), The extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications, Wiley, New York.


  • There are currently no refbacks.

Copyright (c) 2003 Aniello Fedullo

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.