Conference Agenda

The use of ordinal patterns (OPs) for analyzing the dependence structure of univariate and continuously distributed processes has gained popularity in recent years. Here, we go one step further and consider the transcripts being computed from successive OPs in the time series. Transcripts constitute a kind of "difference" between successive OPs and thus naturally relate to two algebraic distances between OPs, the Cayley and Kendall distance. We transform the original time series into a sequence of transcripts or distances, respectively, and derive important stochastic properties thereof. We show that these properties differ substantially between different types of original process. This motivates to develop various statistics based on transcripts and algebraic distances in order to investigate the dependence structure of the original process. In particular, we derive the asymptotic distribution of these statistics under the null hypothesis of serial independence, which is then used to develop nonparametric tests for serial dependence. A simulation study shows that these novel dependence tests have appealing power properties, often outperforming the former OP-based dependence tests. We conclude with a real-world data example, where we illustrate the application and interpretaion of the proposed approaches in practice.