The Spectral Analysis Of Time-Series

The Spectral Analysis of Time-Series Author(s): G. M. Jenkins and M. B. Priestley Source: Journal of the Royal Statistical Society. Series B (Methodological), Vol. 19, No. 1 (1957), pp. 1-12 Published by: Blackwell Publishing for the Royal Statistical Society Stable URL: http://www.jstor.org/stable/2983992 Accessed: 04/10/2010 11:48
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Journalof the Royal StatisticalSociety
SERIES B
(METHODOLOGICAL)

Vol. XIX, No. 1, 1957

ON SYMPOSIUM SPECTRAL APPROACH TIME SERIES TO

[Held before RESEARCH the SECTION theROYAL of STATISTICAL SOCIETY.
in November 1956, H. E. DANIELS theChair] 7th, Dr.
PAGE

The SpectralAnalysisof Time Series. G. M. JENKINS M.B. PRIESTLEY and

.
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1 13

Process. On Estimating Spectral the DensityFunctionof a Stochastic Z. A. LOMNICKI and S. K. ZAREMBA . . . . . . . . . . . Curve and Periodogram Smoothing.P. WHiTrLE .
THE SPECTRAL OF ANALYSIS TIME-SERIES and M. B. PRIESTLEY* By G. M. JENKINS RoyalAircraft Establishment, Farnborough SUMMARY

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38

(i) A REVIEW beenmadeofspectral has branches analysisitsrelation other and with oftime-series analysis. A detailed of account beengiven themethods has available forestimating spectral the and the density, bandspectrum theintegrated spectrum; two estifor suggestions have also been made forconfidence intervals the latter mators. (ii) Emphasis beenlaid throughout has upon thedifficulties which metin are and structure beenindicated.In applicationspractice gapsin thetheoretical have to physical is it that statistical problems, is suggested an empirical approach not and more realistic of enough itself that by descriptions eachparticular phenomenon shouldbe attempted. (iii) Reference already has beenmadein Section to a sampling 9 investigation it in which is proposed applythetechniques to mentioned thispaperto a large in of series numberartificially constructed ofthetype given (1). by
1. Nature of the Problem

The rawdata consist a time-series of which maybe essentially discrete time in (with perhaps a certain amount arbitrariness thechoiceofinterval of in about length), maybe presented the or of form a trace, which in case it is necessary readit at intervals timeAt which to of haveto be decided In before-hand. bothcases,we are left awith sequence {xt}, t = 1, 2, . . ., n which to is subjected analysis. In thefollowing withthis to for paper,it is proposed review existing the techniques dealing with to of problem special reference theanalysis thespectrum.
2. Introduction

It is assumed longterm that trends either are absent elsehavebeenremoved or from series. the Thelatter case is unsatisfactory very since little known...