Bispectral-Based Goodness-of-Fit Tests of Gaussianity and Linearity of Stationary Time Series

Spectral domain tests for time series linearity typically suffer from a lack of power compared to time domain tests. We present two tests for Gaussianity and linearity of a stationary time series. The tests are two-stage procedures applying goodness-of-fit techniques to the estimated normalized bispectrum. We illustrate the performances of the tests are competitive with time domain tests. The new tests typically outperform Hinich's (1982 Hinich , M. J. ( 1982 ). Testing for Gaussianity and linearity of a stationary time series . J. Time Ser. Anal. 3 : 169 – 176 .[Crossref] , [Google Scholar]) bispectral based test, especially when the length of the time series is not large.