Testing that a stationary time-series is Gaussian: time-domain vs. frequency-domain approaches

Several frequency-domain and time-domain procedures for testing that a stationary time-series are Gaussian are presented. Closed-form expressions of the asymptotic distribution of the test statistics under the null hypothesis of Gaussianity are derived. These procedures are then compared and assessed in two typical examples of applications (i) the detection of additive non-Gaussian outliers in stationary Gaussian noise with unknown covariance and (ii) the detection of the presence of contaminating values from non-symmetric distributions.