Time Series Analysis

Time Series Analysis (Speaker: N. Marwan)

Data analysis is a scientific field with increasing importance. Its purpose is to obtain useful information from measurements or simulation results and to justify conclusions. The classical linear data analysis methods were enriched by modern non-linear concepts in the last decades, like estimations of dimensions, fractal properties, Lyapunov exponents, entropy measures etc. Our intentions are to develop modern approaches of data analysis which can be used on specific problems, as occuring, e.g., in the analysis of palaeo-climate data. Here we follow a wide interdisciplinary concept and have experience on the interdisciplinary application of modern non-linear analysis tools. In this sense, we collaborate, e.g., with the RD 1-3 and other groups at GFZ, AWI or UP.

A modern approach of non-linear data analysis considers, e.g., the recurrence structure within the data. A powerful and versatile tool for studying recurrences is the "recurrence plot" and its quantification. The concept of recurrence plots has been shown to be rather successful for the analysis of short and non-stationary data, either time series or even images. Recurrence plots have been used to detect similarities in climate teleconnections in past and today, or to find transitions in climate regimes, as in the Asian monsoonal circulation. They also provide techniques for the detection of directed interrelations or even synchronisation between different systems and have the potential to enrich the concept of complex networks.

We expect a further progress on recurrence plot based techniques in the future. For instance, we are working on statistical tests for this method and to derive similarities between the both concepts of recurrence plots and complex networks. Moreover, recurrence plots will provide additional techniques for creating complex networks.

A similar approach as the recurrence analysis is the reconstruction of complex networks from a time series. This rather new development has several interesting new potentials and is a hot topic in the field.

Another aim is to develop a toolbox of modern methods for the analysis of complex systems. This toolbox is generally available and contains already several R and Matlab packages for non-linear correlation analysis, synchronisation analysis, system identification, filtering, etc.