The discussion centers on the calculation of mutual information between two chaotic time series, x(t) and y(t). Participants explore the concepts of mutual information and cross correlation, particularly in the context of chaotic dynamical systems.
There is no consensus on the interpretation of "mutual information" versus "cross correlation," with participants presenting differing views on the relevance and application of each concept in the context of chaotic time series.
Participants have not resolved the definitions and implications of mutual information and cross correlation, particularly in relation to chaotic systems. The discussion reflects varying levels of familiarity with information theory as it applies to chaotic dynamics.
Actually finding correlation would only help us find any linear correlations but chaotic time series means non-linear correlations as well. For that we need to calculate the mutual information.FactChecker said:Not sure what you mean by "mutual information". Since they are both chaotic, I assume that you are looking for their cross correlation. The cross correlation is a series of numbers, ci, i=0, ±1, ±2, ±3, ..., that are the correlations between xj and yj+i. If there is a linear combination of cross correlations that is statistically significant, then the two series are probably related in some way. There are software statistical packages that you can use to obtain the cross correlations.
Sorry. It sounds like you are really talking about information theory of chaotic systems. I have no knowledge on the subject.phymat Godara said:Actually finding correlation would only help us find any linear correlations but chaotic time series means non-linear correlations as well. For that we need to calculate the mutual information.