A list of new tests for serial dependence based on ordinal patterns are provided. These new methods rely exclusively on the order structure of the data sets. Hence, the novel tests are stable under monotone transformations of the time series and robust against small perturbations or measurement errors. The standard asymptotic distributions are given, and their finite sample behavior under linear and non-linear departures from the null of independence are studied. Moreover, it is proved that under mild conditions, any ordinal-pattern-based test is nuisance free, which is appealing for modelling, as these tests can eventually be used as misspecification tests.
This property is also analyzed for finite samples and illustrated through an empirical application. Much of the discussion is based on a detailed combinatorial analysis of ordinal pattern probabilities
