Asymptotically invariant Gaussianity test for causal invertible time series

This paper introduces a Gaussianity test for causal invertible time series. It is based on a quadratic form in differences between sample means and expected values of certain finite memory nonlinear functions of the estimated innovation sequence. The test has, by construction, an interesting property: under reasonable assumptions on the regularity of the stationary process, it is asymptotically invariant with respect to the spectral density of the process. Monte-Carlo experiments are included to illustrate the proposed approach