On the Use of Higher-Order Statistical Tests in the Analysis of Time Series Associated with Space Data. Utilisation de Tests Basés sur des Statistiques D’Ordre Supérieur dans L’Analyse de Séries Temporelles Mesurées dans L’Espace

On the Use of Higher-Order Statistical Tests in the Analysis of Time Series Associated with Space Data.

Utilisation de Tests Basés sur des Statistiques D’Ordre Supérieur dans L’Analyse de Séries Temporelles Mesurées dans L’Espace

A. Masson B.B. Shishkov  F. Lefeuvre 

Laboratoire de Physique et Chimie de l’Environnement, Centre National de la Recherche Scientifique, 45071 Orléans, Cedex 2, France

Page: 
59-78
|
Received: 
5 March 1999
|
Accepted: 
N/A
|
Published: 
28 February 2001
| Citation

OPEN ACCESS

Abstract: 

Tests of hypotheses based on Higher Order Statistics (HOS) are reviewed in the particular context of the identification of nonlinear processes in space plasma. The time series under study are associated with the measurements of electric or/and magnetic field components, or/and counting rates of particles. The basic principles of HOS techniques are reviewed. A general and unified procedure is suggested in order to construct statistical tests: (1) for detecting a non-gaussian or transient signal in a gaussian (or non-gaussian) noise, (2) testing a stochastic time series for non-gaussianity (including non-linearity), (3) studying non-linear wave interactions by using the kth-order coherency function. Asymptotic theory of estimates of the kthorder spectra is implemented in a digital signal processing framework. The effectiveness of the signal detection algorithms is demonstrated through computer simulations. Examples of application on the analysis of satellite data are given.

Résumé

Des tests d’hypothèses basés sur des statistiques d’ordre supérieur sont revus dans le contexte particulier de l’identification de processus non-linéaires dans les plasmas spatiaux. Les séries temporelles étudiées sont associées à la mesure de composantes du champ électrique et/ou magnétique d’ondes ou de turbulences, et/ou de données particules. Les principes de base des statistiques d’ordre supérieur sont brièvement rappelés. Une procédure générale et unifiée est suggérée afin de construire des tests statistiques permettant : (1) de détecter des signaux non-gaussiens ou transitoires au sein d’un bruit gaussien (ou non-gaussien), (2) de tester si une série temporelle est associée ou non à un processus stochastique issu d’un processus non-linéaire, (3) d’étudier des interactions non-linéaires à plusieurs ondes par l’utilisation de la fonction de cohérence d’ordre k. La théorie asymptotique des estimés des spectres d’ordre k est mise en œuvre dans le cas discret. L’efficacité des algorithmes de détection est démontrée par le biais de simulations numériques. Des exemples d’applications à des données satellites sont présentés.

Keywords: 

Higher-order statistics; non-linear phenomena; transient phenomena; space plasmas.

Mots clés

Statistiques d’ordre supérieur ; phénomènes non linéaires ; phénomènes transitoires ; plasmas spatiaux.

1. Introduction
2. General Background
3. Statistical Tests Based on HOS: Detection Scheme and HOS Estimators
4. Detection of Nongaussian Signals by Third-Order Spectral Analysis
5. Testing for Linearity of Stationary Time Series
6. Detecting a Transient Signal by Bispectral Analysis
7. Applications of the HOS Technique to Nonlinear Wave-Wave Interactions
8. Applications to Satellite Data
9. Conclusion
Notations and abbreviations
Appendix
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