Mutual information between two time series.

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.
  • #1
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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  • #2
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.
 
  • #3
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.
 
  • #4
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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1. What is mutual information between two time series?

Mutual information is a measure of the statistical dependence between two time series. It quantifies how much information is shared between the two series, and can be used to determine the strength of their relationship.

2. How is mutual information calculated for two time series?

Mutual information is typically calculated using mathematical formulas, such as the Shannon entropy formula and the joint entropy formula. These formulas take into account the probability distributions of the two time series to determine the amount of shared information.

3. What is the significance of mutual information in time series analysis?

Mutual information is an important tool in time series analysis as it provides a way to measure the relationship between two time series that may not be linearly related. It can also be used to identify patterns and dependencies between the two series, which can aid in forecasting and prediction.

4. How can mutual information be used in feature selection for time series data?

Mutual information can be used as a feature selection method in time series data by identifying the most informative features based on their relationship with the target time series. This can help to reduce the dimensionality of the data and improve the performance of machine learning models.

5. Can mutual information be applied to non-time series data?

Yes, mutual information can be applied to any type of data, not just time series. It is a general measure of statistical dependence and can be used to quantify the relationship between any two variables, whether they are continuous, discrete, or time series.

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