# Mutual information between two time series.

• I
• Prakhar Godara
In summary, the conversation is discussing the calculation of mutual information between two chaotic time series. The speaker suggests using cross correlation to find any linear correlations, but notes that chaotic time series may also have non-linear correlations that require calculating mutual information. They mention the use of software statistical packages for obtaining cross correlations and admit to not having knowledge on the information theory of chaotic systems.

#### Prakhar Godara

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.

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.

• Prakhar Godara