A tuning parameter free test for properties of space-time covariance functions

We propose a new nonparametric test to test for symmetry and separability of space-time covariance functions. Unlike the existing nonparametric tests, our test has the attractive convenience of being free of choosing any user-chosen number or smoothing parameter. The asymptotic null distributions of the test statistics are free of nuisance parameters and the critical values have been tabulated in the literature. From a practical point of view, our test is easy to implement and can be readily used by the practitioner. A Monte-Carlo experiment and real data analysis illustrate the finite sample performance of the new test.