On the reliability of some tests on type of non-separability and type of class of covariance models

In the literature, various tests for evaluating some characteristics of space-time covariance functions, such as symmetry and separability, are widely used. Recently, in case of rejection of the separability hypothesis, innovative tests have been proposed for evaluating the type of non-separability of space-time covariance functions and testing some well known classes of non-separable positive or negative covariance function models. In this paper a study on simulated data is proposed in order to assess the performance of the tests on the type of non-separability and on the classes of covariance functions.