Testing that a multivariate stationary time-series is Gaussian

These tests are based on quadratic form in deviations of certain sample statistics from their ensemble counterpart, minimised with respect to the unknown parameters. They are shown to converge under the null hypothesis to a chi-squared distribution. A specific test is developed on the basis of the difference between the sample estimate and the ensemble average characteristic functions. Preliminary results demonstrate the discriminative power of the test against various types of alternatives