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.