Use of Higher-Order Statistical Tests in the Analysis of Time Series Associated with Space Data
Publication date: 27 June 2001
Authors: Masson, A., et al.
Journal: Tairement du Signal
Volume: 18
Page: 59-78
Year: 2001
Tests of hypotheses based on Higher Order Statistics (HOS) are reviewed in the particular context of the identification of non-linear processes in space plasma. The time series under study are associated with the measurement of electric or/and magnetic field components, or/and counting rates of articles. 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-wave interactions by using the kth-order coherency function. Asymptotic theory of estimates of the kth-order 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.