Methoden vergleichen

	Convergent Cross Mapping (CCM)	Rekurrenzanalyse (RQA)	Transfer Entropy
Fachgebiet	Kausale Inferenz	Komplexe Systeme	Kausale Inferenz
Familie	Machine learning	Machine learning	Machine learning
Entstehungsjahr	2012	2007	2000
Urheber	George Sugihara et al.	Marwan, Romano, Thiel & Kurths	Thomas Schreiber
Typ	Nonlinear time-series causality test	Nonlinear time-series characterization	Non-parametric information-theoretic measure
Wegweisende Quelle	Sugihara, G., et al. (2012). Detecting causality in complex ecosystems. Science, 338(6106), 496–500.	Marwan, N., Romano, M. C., Thiel, M., & Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5–6), 237–329.	Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–464.
Aliasnamen	CCM, Cross-Convergent Mapping, Empirical Dynamic Modelling Causality, Yakınsak Çapraz Haritalama	RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi	Schreiber Information Transfer, Directed Information Flow, Conditional Mutual Information (directed), Transfer Entropisi
Verwandt	3	2	3
Zusammenfassung	Convergent Cross Mapping (CCM) is a nonlinear, state-space method for detecting causality between time-series variables embedded in a shared dynamical system. Introduced by George Sugihara and colleagues in their landmark 2012 Science paper, CCM exploits Takens' embedding theorem: if variable X causally influences Y, the historical record of Y contains enough information to recover the states of X. Causality is confirmed when cross-map skill improves—converges—as the time-series library grows longer.	Recurrence Quantification Analysis (RQA) is a nonlinear method for characterizing the dynamics of a time series by quantifying the small-scale structure of its recurrence plot. Introduced in its modern, comprehensive form by Marwan, Romano, Thiel, and Kurths in 2007, RQA extracts scalar measures — such as recurrence rate, determinism, laminarity, and Shannon entropy — that capture periodicity, chaos, stationarity, and transitions in complex dynamical systems.	Transfer Entropy (TE) is a non-parametric, information-theoretic measure of directed statistical dependence between two time series, introduced by Thomas Schreiber in 2000. Grounded in Shannon entropy, it quantifies how much information the past of one process Y reduces uncertainty about the next state of another process X, beyond what X's own past already provides. Unlike linear correlation or Granger causality, TE captures nonlinear interactions and requires no model assumptions about the underlying dynamics.