Spectral analysis of a stationary stochastic process

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spectral analysis of a time series

The same as spectral decomposition of a stationary stochastic process (cf. Spectral decomposition of a random function).

A set of statistical methods that enables one to estimate the value of the spectral density of a stationary stochastic process from the observed data of one (or several) realization(s) of this process (see [1][5]). See also Statistical problems in the theory of stochastic processes; Periodogram; Spectral density, estimator of the; Maximum-entropy spectral estimator; Spectral estimator, parametric.


[1] G.M. Jenkins, D.G. Watts, "Spectral analysis and its applications" , 1–2 , Holden-Day (1968)
[2] D.G. Childers (ed.) , Modern spectrum analysis , IEEE (1978)
[3] S.S. Haykin (ed.) , Nonlinear methods of spectral analysis , Springer (1983)
[4] S.M. Kay, S.L. Marple, "Spectrum analysis - A modern perspective" , Proc. IEEE , 69 : 11 (1981) pp. 1380–1419 (Erratum: Vol. 70 (1982), 120; Comments: Vol. 71 (1983), 776–779; 1324–1325)
[5] "Spectral estimation" Proc. IEEE , 70 : 9 (1982) ((Special Issue))
[6] S.M. Kay, "Modern spectral estimation" , Prentice-Hall (1987)
[7] S.L. Marple, "Digital spectral analysis with applications" , Prentice-Hall (1987)
How to Cite This Entry:
Spectral analysis of a stationary stochastic process. A.M. Yaglom (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098