In this paper we had made an attempt to incorporate the results from the theory of square Gaussian random variables in order to construct the goodness of fits test for random sequences (time series). We considered two versions of such tests. The first one was designed for testing the adequacy of the hypotheses on expectation and covariance function of univariate non-centered sequence, the other one was constructed for testing the hypotheses on covariance of the multivariate centered sequence. The simulation results illustrate the behavior of these tests in some particular cases.