Time Series Analysis (TSA)
Speaker: Norbert Marwan
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
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 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.
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).
- K. Rehfeld, N. Marwan, S. F. M. Breitenbach, J. Kurths: Late Holocene Asian summer monsoon dynamics from small but complex networks of paleoclimate data, Climate Dynamics, 41(1), 3–19 (2013).
- K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths: Comparison of correlation analysis techniques for irregularly sampled time series, Nonlinear Processes in Geophysics, 18(3), 389–404 (2011).
Schematic illustration of Momentary
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.
- J. Runge, V. Petoukhov, J. Kurths: Quantifying the strength and delay of climatic interactions: the ambiguities of cross correlation and a novel measure based on graphical models, Journal of Climate, 27(2), 720-739 (2014).
- J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths: Geometric signature of complex synchronisation scenarios, Europhysics Letters, 102(3), 30007 (2013).
- B. Goswami, N. Marwan, G. Feulner, J. Kurths: How do global temperature drivers influence each other? – A network perspective using recurrences, European Physical Journal – Special Topics, 222, 861–873 (2013).
- N. Malik, B. Bookhagen, N. Marwan, J. Kurths: Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks, Climate Dynamics, 39(3–4), 971–987 (2012).
- J. Runge, J. Heitzig, N. Marwan, J. Kurths: Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy, Physical Review E, 86, 061121 (2012).
- Y. Zou, M. C. Romano, M. Thiel, N. Marwan, J. Kurths: Inferring Indirect Coupling by Means of Recurrences, International Journal of Bifurcation and Chaos, 21(4), 1099–1111 (2011).
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 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.
- N. Marwan, S. Schinkel, J. Kurths: Recurrence plots 25 years later – Gaining confidence in dynamical transitions, Europhysics Letters, 101, 20007 (2013).
- J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, J. Kurths: Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution, Proceedings of the National Academy of Sciences, 108(51), 20422–20427 (2011).
- R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, J. Kurths: Recurrence-based time series analysis by means of complex network methods, International Journal of Bifurcation and Chaos, 21(4), 1019–1046 (2011).
- N. Marwan: How to avoid potential pitfalls in recurrence plot based data analysis, International Journal of Bifurcation and Chaos, 21(4), 1003–1017 (2011).
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 WorldOctober 2015 – March 2020, Funded by: DFG - Deutsche ForschungsgemeinschaftContact: Marwan, Norbert
- PPP Norwegen
Nichtlineare Charakterisierung spätholozäner KlimavariabilitätJanuary 2016 – December 2017, Funded by: DAAD - Deutscher Akademischer Austausch DienstContact: Donner, Reik
- PPP Tschechien
Charakterisierung komplexer Kausalstrukturen im KlimasystemFebruary 2015 – January 2017, Funded by: DAAD - Deutscher Akademischer Austausch DienstContact: Donner, Reik
QUantitative paleoEnvironments from SpeleoThemsJanuary 2016 – December 2019, Funded by: EU, H2020Contact: Marwan, Norbert
- SME Voucher
Model reduction for CO(2) optimisationSeptember 2015 – February 2016, Funded by: Climate-KICContact: Hellmann, Frank
- Sunda Shelf
Gradual Environmental Change versus Single Catastrophe - Identifying Drivers of Mammalian EvolutionApril 2013 – March 2016, Funded by: Leibniz-GemeinschaftContact: Marwan, Norbert