Testing for Dependence by Using Ordinal Patterns: an Introduction

About 20 years ago, ordinal patterns have been introduced as a simple, robust, and flexible tool for analyzing the serial dependence structure of univariate real-valued stochastic processes. If applied to continuously distributed processes, one can derive non-parametric tests of the null hypothesis that the process is independent and identically distributed. Recently, also more sophisticated tasks for dependence tests have been considered: serial dependence in a discrete-valued process, the sequential monitoring of serial dependence, cross-dependence in a multivariate process, and spatial dependence in a random field. This talk provides an introduction to the aforementioned topics together with illustrative examples, and it concludes by outlining perspectives for future research.