Time Series Analysis (TSA)

We develop and provide innovative and powerful tools and concepts for the other research domains for a better understanding of the system Earth.

Speaker: Norbert Marwan

Team members: Reik Donner,  Deniz Eroglu, Ankit Agarwal,Ugur Öztürk, Hauke Krämer, Bedartha Goswami

Research background

Real world processes are complex and appear to be chaotic, i.e., their predictability is limited. Nonlinear theory offers new approaches for the development of modern data analysis techniques which can shed light on specific features in the dynamics of complex systems where standard or linear methods are not able to study them.

Example: Challenges in palaeoclimate research

Krem Mawmluh

Cave Mawmluh in the Meghalaya district, India.
Several speleothems from this and nearby caves
have been analysed to study the past Asian

Recent projects are collecting and extending the data archive of the palaeoclimate. New high precision records, e.g., such from stalagmites, offer new insights into the climate system or extreme events in the past that have not been available before on such high-resolution time-scales.

However, such geological archives come with specific problems, such as time uncertainties and irregular sampling – challenges that hamper the application of standard methods or introducing nontrivial biases in the final results. Moreover, the definition of extreme climate events on the basis of geological archives is difficult, as it depends strongly on the time scale and since geological archives usually aggregate and integrate the environmental conditions over a longer period of time. There is a big need in methods which can be applied on such kind of data to derive reliable information about climate variability and the distribution of extremes while properly taking into account uncertainties.


Recurrence network for Rössler in 2D
Recurrence network for the Rössler

We are developing and adopting methods of non-linear time series analysis for direct application to data with irregular sampling and with special focus on time uncertainties. This includes simple methods like kernel-based correlations, but also more complex methods like conditional mutual information and recurrence based measures. We further develop methods for studying the recurrence structure and extreme events in data. New definitions of recurrence and extremes are in development for the particular consideration of time uncertainties. The recurrence concept is under extension to study spatio-temporal data. Moreover, we work on the development of methods for studying couplings, interrelations, and causal directions within extended systems. This research will also be a basis for the reconstruction of complex networks and networks of networks.

Research Highlights

Development of statistical association methods (correlation and mutual information) for the direct application on irregularly sampled time series. This development is the core for the subsequent spatio-temporal investigation of palaeo-climate data by complex networks (palaeo-climate networks).

Momentary Information Transfer

Schematic illustration of Momentary
Information Transfer.


Several approaches for the investigation of direct and indirect links, causal couplings, or coincidences of special events have been developed, critically tested, and finally applied to climate data, answering questions about differences in the spatial patterns of extreme monsoonal rainfall in India and South America, interrelations between the East Asian Summer monsoon and Indian Summer monsoon, or causal relationships between global warming, solar and volcanic activity, and human impact.


Schema for absolute age

Schema for the transfer of age uncertainties
to uncertainties in the proxy domain.

Introduction of a framework for dealing with time uncertainties in palaeo-climate proxy records (COPRA). This approach was the basis for the discussion about the socio-economic climate impact in the Mayan civilization.

  • S. F. M. Breitenbach, K. Rehfeld, B. Goswami, J. U. L. Baldini, H. E. Ridley, D. Kennett, K. Prufer, V. V. Aquino, Y. Asmerom, V. J. Polyak, H. Cheng, J. Kurths, N. Marwan: COnstructing Proxy-Record Age models (COPRA), Climate of the Past, 8, 1765–1779 (2012).
  • Science cover story: D. J. Kennett, S. F. M. Breitenbach, V. V. Aquino, Y. Asmerom, J. Awe, J. U. L. Baldini, P. Bartlein, B. J. Culleton, C. Ebert, C. Jazwa, M. J. Macri, N. Marwan, V. Polyak, K. M. Prufer, H. E. Ridley, H. Sodemann, B. Winterhalder, G. H. Haug: Development and Disintegration of Maya Political Systems in Response to Climate Change, Science, 338(6108), 788–791 (2012).


Recurrence plot with distribution
Recurrence plot and merged distribution of
the diagonal lines.

Extending the standard recurrence analysis by the complex network approach, providing additional measures of complexity for the study of dynamical transitions in complex systems (recurrence networks). Moreover, the recurrence analysis techniques has been critically revisited and approaches for significance tests suggested.

Toolbox for Complex Systems (TOCSY)

With Toolboxes for Complex Systems we provide a compilation of innovative methods for modern nonlinear data analysis. These methods were developed during our scientific research and cover recurrence analysis, causality investigations, filter procedures, time series analysis for irregularly sampled time series, etc.


Natural Hazards and Risks in a Changing World
October 2015 – March 2020, Funded by: DFG - Deutsche Forschungsgemeinschaft
Contact: Marwan, Norbert
PPP Norwegen
Nichtlineare Charakterisierung spätholozäner Klimavariabilität
January 2016 – December 2017, Funded by: DAAD - Deutscher Akademischer Austausch Dienst
Contact: Donner, Reik
QUantitative paleoEnvironments from SpeleoThems
January 2016 – December 2019, Funded by: EU, H2020
Contact: Marwan, Norbert




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