Improved bispectrum based tests for Gaussianity and linearity

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. (C) 2009 Elsevier B.V. All rights reserved.