Trispectral analysis of stationary random time series
John W. Dalle Molle, Melvin J. Hinich · The Journal of the Acoustical Society of America · 1995
This paper investigates the statistical properties of the trispectrum. The trispectrum is the Fourier transform of the fourth-order joint lagged cumulant of a zero-mean stationary random time series. A complete representation of the principal domain of the trispectrum derived from its inherent symmetries is detailed. The large sample variance for a consistent estimator of the trispectrum is presented and used in the development of the fourth-order generalizations of the bispectrum-based Hinich tests of Gaussianity and linearity. A test for stationarity is developed using an amended version of the trispectrum-based test of Gaussianity. An arithmetic frame-averaging procedure is used to compute consistent trispectral estimates for a zero-mean bandlimited real-valued stationary random process. The trispectral-based tests are applied to time series of ship noise recorded by a sonobouy in the Eastern Atlantic Ocean.