Improved bispectrum based tests for Gaussianity and linearity

Authors:
Yngve Birkelund;Alfred Hanssen
Affiliations:
Department of Physics and Technology, University of Tromsø, NO-9037 Tromso, Norway;Department of Physics and Technology, University of Tromsø, NO-9037 Tromso, Norway
Venue:
Signal Processing
Year:
2009

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Abstract

The classical bispectrum based tests for linearity of time series are based on Gaussian asymptotics and a suboptimal smoothing in the bispectral domain. We show that the resulting classical tests may lead to vastly incorrect significance levels for non-Gaussian time series. This implies that a non-Gaussian linear time series may incorrectly be classified as non-linear. The purpose of this paper is to propose simple yet accurate tests for Gaussianity and linearity. The improved tests are derived through: (1) an optimal hexagonal smoothing in the bispectral domain, (2) the construction of simple and intuitive bispectrum based test statistics, and (3) determination of correct significance levels through a new skewness preserving scheme for linear surrogate data. The superiority of the proposed tests is demonstrated through extensive Monte Carlo simulations using relevant synthetic data.