{"id":3461,"date":"2023-12-30T09:42:05","date_gmt":"2023-12-30T08:42:05","guid":{"rendered":"https:\/\/www.um.sav.sk\/en\/?p=3461"},"modified":"2024-01-30T13:35:29","modified_gmt":"2024-01-30T12:35:29","slug":"1-problems-of-causal-analysis-of-deterministic-time-series","status":"publish","type":"post","link":"https:\/\/www.um.sav.sk\/en\/selected-results\/1-problems-of-causal-analysis-of-deterministic-time-series\/","title":{"rendered":"Problems of causal analysis of deterministic time series"},"content":{"rendered":"

Investigators:<\/strong> Anna Krakovsk\u00e1, Martina Chvostekov\u00e1, Jozef Jakub\u00edk<\/em><\/p>\n

Identifying causal relationships in measured time series is a research topic that we have been working on intensively for several years. This year we have focused on discovering causality in cases where traditional tools such as the Granger test, successful for example in autoregressive processes, are not applicable [3], [4]. This is particularly the case for processes that are well modelled as deterministic dynamical systems.
\nWe derive a fast and simple method for estimating the fractal complexity of the systems under study, which opens up new possibilities for the study of the synchronization process and efficient causal analysis of long time measurements dominated by deterministic dynamics. We have published the proposed methodology in [1], presented it at an international conference [5], [6] and published the corresponding MatLab code in [7].
\nDeterminism in data is also problematic in the context of the so-called first principle of causality, which is the rule that cause always precedes effect. Although one might expect that, once time series are rotated, causality detection methods simply swap cause and effect, our analysis in [2] shows that no such swap occurs in the case of deterministic series. We have explored the reasons for this apparent paradox using both numerical and theoretical methods.<\/p>\n

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Fig. Correlation dimensions D2 of systems X, Y and their combinations for increasing strength of connection C. Comparison of the D2 estimates reliably reveals that for C>0 X causally affects Y and allows identification of the onset of synchronization.<\/em><\/p>\n

Related projects:<\/strong> \u00a0 Addressed in the framework of projects APVV-21-0216, VEGA nr. 2\/0096\/21 and VEGA nr. 2\/0023\/22.<\/p>\n

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Publications:
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