On the Use of Complexity Algorithms: a Cautionary Lesson from Climate Research

Complexity algorithms provide information about datasets which is radically different from classical moment statistics. Instead of focusing on the divergences from central values, they quantify other characteristics such as order, pattern repetitions, or the existence of attractors. However, those analyses must be done with the proper statistical treatment, which is, unfortunately, not always the case. In this contribution, I provide an example of the hazards of applying complexity measures without sufficient care by correcting a previously published analysis that aimed to quantify the complexity of climate. I clarify some misconceptions about the use of Sample Entropy and revise the incorrect assessments and conclusions drawn from the previous misapplication of the methods.