Characteristic function-based hypothesis tests under weak dependence

In this article we propose two consistent hypothesis tests of L2L2-type for weakly dependent observations based on the empirical characteristic function. We consider a symmetry test and a goodness-of-fit test for the marginal distribution of a time series. The asymptotic behaviour under the null as well as fixed and certain local alternatives is investigated. Since the limit distributions of the test statistics depend on unknown parameters in a complicated way, we suggest to apply certain parametric bootstrap methods in order to determine critical values of the tests.