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.

本研究提出一种全新的检验流程，用于检测时间序列中的序列相依性。该方法仅基于数据的序数结构构建，且明确允许所考量的数据窗口中存在结（ties）。据此，我们采用广义序数模式，即凯莱排列（Cayley permutations）。与经典情形不同，在序列独立的原假设下，该模式的分布并非均匀分布。在本研究提出的新框架中，需将底层分布纳入考量范畴，我们通过自助法（bootstrap procedure）解决了这一问题。仿真实验与两个真实数据集案例验证了本方法的适用性。