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Linear least squares prediction in non-stochastic time series

Published online by Cambridge University Press:  01 July 2016

P. D. Finch
P. D. Finch*
Affiliation:
Monash University
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Extract

Many problems arising in the physical and social sciences relate to processes which happen sequentially. Such processes are usually investigated by means of the theory of stationary stochastic processes, but there have been some attempts to develop techniques which are not subject to the conceptual difficulties inherent in the probabilistic approach. These difficulties stem from the fact that in practice one is often restricted to a single record which, from the probabilistic point of view, is only one sample from an ensemble of possible records. In some instances such a viewpoint seems artificial, and for some time series it is questionable whether any objective reality corresponds to the idea of an ensemble of possible time series. For example, as noted in Feller (1967), a theory of probability based on a frequency interpretation cannot meaningfully attach a probability to a statement such as “the sun will rise tomorrow”, because to do so one would have to set up a conceptual universe of possible worlds.

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Type
Research Article
Information
Advances in Applied Probability , Volume 1 , Issue 1 , Spring 1969, pp. 111 - 122
Copyright
Copyright © Applied Probability Trust 

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References

Bass, J. (1962) Les Fonctions Pseudo-Aléatoires. Mém. des Sc. Math. CLIII. Gauthier-Villars, Paris.Google Scholar
Doob, J. (1963) Stochastic Processes. Wiley & Sons Inc., New York.Google Scholar
Feller, W. (1967) An Introduction to Probability Theory and its Applications. Vol. 1, Third Ed. Wiley, New York.Google Scholar
Furstenburg, H. (1960) Stationary Processes and Prediction Theory. Ann. of Math. Studies 44. Princeton.Google Scholar
Kolmogorov, A. N. (1941a) Stationary sequences in Hilbert space. Bull. Moscow State Univ. 2, No. 6.Google Scholar
Kolmogorov, A. N. (1941b) Interpolation and extrapolation of stationary random sequences. Izv. Akad. Nauk. SSSR Ser. Mat. 5, 3.Google Scholar
Marcinkiewicz, J. (1939) Une remarque sur les espaces de M. Bésikovitch. C. R. Acad. Sci. Paris 208, 157.Google Scholar
Masani, P. (1963) Review of Furstenburg (1960). Bull. Amer. Math. Soc. 69, 195–206.CrossRefGoogle Scholar
Wiener, N. (1930) Generalized harmonic analysis. Acta Math. 55, 117–258.Google Scholar
Wiener, N. (1949) The Extrapolation, Interpolation and Smoothing of Stationary Time Series. M.I.T. Press, Cambridge, Mass.CrossRefGoogle Scholar
Yaglom, A. M. (1962) Stationary Random Functions. Prentice-Hall Inc., New Jersey.Google Scholar