Open Access
December, 1948 On Prediction in Stationary Time Series
Herman O. A. Wold
Ann. Math. Statist. 19(4): 558-567 (December, 1948). DOI: 10.1214/aoms/1177730151


In time series analysis there are two lines of approach, here called the functional and the stochastic. In the former case, the given time series is interpreted as a mathematical function, in the latter case as a random specimen out of a universe of mathematical functions. The close relation between the two approaches is in section 2 shown to amount to a genuine isomorphism. Considering the problem of prediction from this viewpoint, the author gives in sections 3-4 the functional equivalence of his earlier theorem on the decomposition of a stationary stochastic process with a discrete time parameter (see [9], theorem 7). In section 5 the decomposition theorem is applied to the problem of linear prediction. Finally in section 6 a few comments are made. Since various aspects of the isomorphism in question are known, this paper might be regarded as essentially expository.


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Herman O. A. Wold. "On Prediction in Stationary Time Series." Ann. Math. Statist. 19 (4) 558 - 567, December, 1948.


Published: December, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0032.41803
MathSciNet: MR27467
Digital Object Identifier: 10.1214/aoms/1177730151

Rights: Copyright © 1948 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1948
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