On goodness-of-fit tests for weakly dependent processes using kernel method

In this paper, we extend some existing goodness-of-fit tests for independent observations using kernel method to tests for weakly dependent processes. The tests considered include: (i) a two sample goodness-of-fit test; (ii) a symmetry test; and (iii) a test for the goodness-of-fit of a parametric density function. We also develop a center-free test for the goodness-of-fit of a parametric density function. We establish the asymptotic normality of the tests under the corresponding null hypotheses and verify their consistency.