Abstract: J. Donath (2019)

Recurrence plots (RPs) are a powerful approach in time series analysis with a wide range of applications. The dynamics underlying the measured time series can be understood by looking at the structures in the RP, which are quantified using re- currence quantification analysis (RQA).

To account for the uncertainties of the time series the RP can be estimated from a series of time-ordered probability densities, resulting in a probabilistic RP (PRP). Applying the RQA to these PRPs poses a challenge. In contrast to a typical RP, which consists of binary entries that form clearly defined structures like vertical or diagonal lines, a PRP is filled with probabilities ranging from zero to one. It, there- fore, lacks a clear definition of an RP line structure, upon which RQA is founded. In this thesis, several approaches aimed at reconstructing an ensemble of RPs from a PRP are investigated. This enables the application of all methods developed for the analysis of RPs, such as the RQA or complex network measures, to the ensemble members. The reconstruction of ensembles instead of single RPs not only takes into account the uncertainties reflected in the probabilities of the PRP but proves essential for the analysis of more complex real-world data. Using model systems and paleoclimatology data it can be shown that the approaches are, in principle, able to identify abrupt transitions in the time series. However, the reconstructed RPs differ in some important aspects from typical RPs. They consist of large recurrence blocks or mostly single points and very short lines, depending on the used reconstruction approach.

Nevertheless, by studying three paleoclimatology datasets with the developed meth- ods, it is possible to estimate the strength of the Asian monsoon in the Holocene and, as a proof of concept, identify many known events. In particular, a link with ice-rafting events in the North Atlantic can be confirmed.

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Recurrence quantification analysis of probabilistic recurrence plots