A random-projection based Gaussianity test for stationary process

In this talk we present a procedure to test if a stationary process is Gaussian. The observation consists in a finite sample of a path of the process. The test is based on the fact (stablished in Cuesta-Albertos et al. (2007)) that, almost surely, a distribution is Gaussian iff a randomly chosen onedimensional projection is Gaussian, thus transforming the problema of testing the infinite-dimensional Gaussianity in testing the Gaussianity of a one-dimensional distribution. Most of known tests only check if the one-dimensional marginals of the process under consideration are Gaussian, thus being at the nominal power against those non-Gaussian alternatives with Gaussian one-dimensional marginals. However, the procedure that we present here is consistent against every alternative (under some regularity conditions). The talk will also include some simulations and the analysis of some real data sets to compare our procedure with some other well-known tests proposed in the literature.