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Goodness-of-fit tests for random sequences incorporating several components

Abstract In this paper we have constructed the goodness-of-fit tests incorporating several components, like expectation and covariance function for identification of a non-centered univariate random sequence or auto-covariances and cross-covariances for identification of a centered multivariate random sequence. For the construction of the corresponding estimators and investigation of their properties we utilized the theory of square Gaussian random variables.