Estimation of interaction strength and direction from short and noisy time series

Abstract

A technique for determination of character and intensity of interaction between the elements of complex systems based on reconstruction of model equations for phase dynamics is extended to the case of short and noisy time series. Corrections, which eliminate systematic errors of the estimates, and expressions for confidence intervals are derived. Analytic results are presented for a particular case of linear uncoupled systems, and their validity for a much wider range of situations is demonstrated with numerical examples. The technique should be useful for the analysis of nonstationary processes in real time, including the situations of significant noise and restrictions on the observation time.

Information Transfer in the Brain: Insights from a Unified Approach

“…On the other hand, Granger causality formalized the notion that, if the prediction of one time series could be improved by incorporating the knowledge of past values of a second one, then the latter is said to have a causal influence on the former. Initially developed for econometric applications, Granger causality has gained popularity also in neuroscience (see, e.g., [9,39,16,27]). A discussion about the practical estimation of information theoretic indexes for signals of limited length can be found in [33].…”

Epilepsy

“…In order to measure the direction of interactions, Rosenblum and Pikovsky proposed a phase-modeling approach [294] that considers a two-dimensional finite Fourier series for both phase variables to approximate -in a least-squares sense -the deterministic parts of the phase dynamics. The asymmetric influence between two systems can then be estimated using the derivatives of the Fourier series, and more recent developments aim at a further improvement of this approach [20,76,166,293,[325][326][327].…”

Synchronization Approach to Analysis of Biological Systems

“…For examples of application to the cardiorespiratory and brain data see [30,32]. Statistical properties of the directionality estimation are considered in [33].…”