# Spectral analysis of a stationary stochastic process

From Encyclopedia of Mathematics

*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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Spectral_analysis_of_a_stationary_stochastic_process&oldid=16841

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098