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In this paper we address the statistical problem of testing if a stationaryprocess is Gaussian. The observation consists in a finite sample path of theprocess. Using a random projection technique introduced and studied inCuesta-Albertos et al. 2007 in the frame of goodness of fit test for functionaldata, we perform some decision rules. These rules really stand on the wholedistribution of the process and not only on its marginal distribution at afixed order. The main idea is to test the Gaussianity on the marginaldistribution of some random linear combinations of the process. This leads toconsistent decision rules. Some numerical simulations show the pertinence ofour approach.

A random-projection based procedure to test if a stationary process is Gaussian