Time-domain procedures for testing that a stationary time-series is Gaussian

Author

Moulines, Eric ; Choukri, Karim

Author_Institution

Dept. of Signal Process., Ecole Nat. Superieure des Telecommun., Paris, France

Volume

44

Issue

8

fYear

1996

fDate

8/1/1996 12:00:00 AM

Firstpage

2010

Lastpage

2025

Abstract

A class of time-domain procedures for testing that a stationary time-series is Gaussian is presented and analyzed. These tests are based on the deviations of the sample value of finite memory nonlinear transformations of the process from their ensemble averaged counterparts. Asymptotic distributions of these tests are derived under the null hypothesis of Gaussianity and under a class of local and fixed alternatives. Specific tests are then developed, based, respectively, on higher order moments and on the characteristic functions. Practical construction of the test statistics is discussed, with a special emphasis on the estimation of the covariance of the sample statistics, which appears to play a key role in the performance of the tests when dealing with `small´ samples

Keywords

Gaussian distribution; Gaussian processes; covariance analysis; estimation theory; higher order statistics; signal sampling; time series; time-domain analysis; Gaussian test; asymptotic distributions; characteristic functions; covariance estimation; finite memory nonlinear transformations; higher order moments; null hypothesis; sample statistics; small samples; stationary time-series; test statistics; time-domain procedures; Convergence; Distribution functions; Equations; Frequency; Gaussian distribution; Gaussian processes; Statistics; Testing; Time domain analysis; Tin;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.533722

Filename

533722