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Goodness-of-fit tests for random sequences incorporating several components. (English) Zbl 1360.62440
Summary: 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.
##### MSC:
 62M07 Non-Markovian processes: hypothesis testing 60G15 Gaussian processes 60G10 Stationary stochastic processes 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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