The Annals of Mathematical Statistics

An Approach to Time Series Analysis

Emanuel Parzen

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 32, Number 4 (1961), 951-989.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177704840

Digital Object Identifier
doi:10.1214/aoms/1177704840

Mathematical Reviews number (MathSciNet)
MR143315

Zentralblatt MATH identifier
0107.13801

JSTOR
links.jstor.org

Citation

Parzen, Emanuel. An Approach to Time Series Analysis. Ann. Math. Statist. 32 (1961), no. 4, 951--989. doi:10.1214/aoms/1177704840. https://projecteuclid.org/euclid.aoms/1177704840


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