Higher-order statistics: laying a myth to rest

The property of the bispectrum that relates to random processes with symmetric probability density functions (PDFs) has often been interpreted to mean that the bispectrum of a stationary random process is zero if the marginal PDF is symmetric regardless of whether the random process is white or colored. It is shown that if the random process is not white, it can still have a non-zero bispectrum even if the marginal PDF is a symmetric function such as the Laplacian PDF or a nearly Gaussian function. Symmetry conditions expressed in terms of the marginal and joint PDFs that guarantee a zero bispectrum are postulated