I Mutual information between two time series.

AI Thread Summary
The discussion centers on calculating mutual information between two chaotic time series, x(t) and y(t). Participants clarify that while cross correlation can identify linear relationships, mutual information is necessary for detecting non-linear correlations inherent in chaotic systems. There is a suggestion that statistical software can assist in obtaining cross correlations, but the focus remains on the need for mutual information. The conversation highlights a gap in knowledge regarding the application of information theory to chaotic systems. Understanding mutual information is essential for analyzing the complexities of chaotic time series relationships.
Prakhar Godara
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So I am studying chaotic dynamical systems and I need to find mutual information between two chaotic time series say x(t) and y(t). Any help would be much appreciated.
 
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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.
 
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.
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.
 
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.
Sorry. It sounds like you are really talking about information theory of chaotic systems. I have no knowledge on the subject.
 
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