Generalized ordinal patterns in discrete-valued time series: nonparametric testing for serial dependence

We provide a new testing procedure to detect serial dependence in time series. Our method is based solely on the ordinal structure of the data. We explicitly allow for ties in the data windows we consider. Consequently, we use generalised ordinal patterns, that is, Cayley permutations. Unlike in the classical case, the pattern distribution is not uniform under the null hypothesis of serial independence. In our new framework, the underlying distribution has to be taken into account and we overcome this problem by a bootstrap procedure. The applicability of our method is supported by a simulation study and two real-world data examples.