Conditional Granger Causality of Diffusion Processes

0480176 - ÚI 2018 RIV DE eng J - Journal Article
Wahl, B. - Feudel, U. - Hlinka, Jaroslav - Wächter, M. - Peinke, J. - Freund, J.A.
Conditional Granger Causality of Diffusion Processes.
European Physical Journal B. Roč. 90, č. 10 (2017), č. článku 197. ISSN 1434-6028. E-ISSN 1434-6036
R&D Projects: GA ČR GA13-23940S; GA MZd(CZ) NV15-29835A
Institutional support: RVO:67985807
Keywords : Granger causality * stochastic process * diffusion process * nonlinear dynamical systems
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 1.536, year: 2017

The statistical concept of Granger causality is defined by prediction improvement, i.e. the causing time series contains unique information about the future of the caused one. Recently we proposed extending this concept to bivariate diffusion processes by defining Granger causality for each point of the state space as the Granger causality of a process obtained by local linearisation. This provides a Granger causality map, well-defined at least in the vicinity of stable fixed points of the deterministic part of the dynamics. This extension has convenient properties, but carries several important limitations. In the current paper we show how the Granger causality of diffusion processes can be further generalized, incorporating in particular the concept of conditional causality. Moreover, we demonstrate the application potential to systems with a more complex attractor structure such as limit cycles or bistability of fixed points.
Permanent Link: http://hdl.handle.net/11104/0276061