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December, 1961 An Approach to Time Series Analysis
Emanuel Parzen
Ann. Math. Statist. 32(4): 951-989 (December, 1961). DOI: 10.1214/aoms/1177704840


It may fairly be said that modern time series analysis is a subject which embraces three fields which while closely related have tended to develop somewhat independently. These fields are (i) statistical communication and control theory, (ii) the probabilistic (and Hilbert space) theory of stochastic processes processing finite second moments, and (iii) the statistical theory of regression analysis, correlation analysis, and spectral (or harmonic) analysis of time series. In this paper it is my aim to show the close relation between these fields and to summarize some recent developments. The topics discussed are (i) stationary time series and their statistical analysis, (ii) prediction theory and the Hilbert space spanned by a time series, and (iii) regression analysis of time series with known covariance function. In particular, I describe a new approach to prediction and regression problems using reproducing kernel Hilbert spaces.


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Emanuel Parzen. "An Approach to Time Series Analysis." Ann. Math. Statist. 32 (4) 951 - 989, December, 1961.


Published: December, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0107.13801
MathSciNet: MR143315
Digital Object Identifier: 10.1214/aoms/1177704840

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 4 • December, 1961
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