This discussion focuses 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 essential for capturing non-linear correlations inherent in chaotic systems. The conversation emphasizes the need for statistical software packages to compute these metrics effectively. Understanding the distinction between linear and non-linear correlations is crucial for analyzing chaotic dynamical systems.
PREREQUISITESThis discussion is beneficial for researchers and analysts working with chaotic dynamical systems, data scientists exploring time series analysis, and statisticians interested in information theory applications.
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.