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As the title implies I am having difficulty differentiating between the correlation matrix and the cross correlation matrix with reference to time series data. Could anyone enlighten me please? Is the only difference that the cross correlation uses a sliding window to calculate the correlation over time whereas the correlation is time independent?

According to wikipedia the cross correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. That is one signal is delayed relative to the other and the correlation between the two is calculated, kind of similar to the autocorrelation but with another signal rather than itself.

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When it comes to correlation, there are several types in the realm of time series analysis.

Cross correlation is only one measure - which is referring to the correlation of one signal with another.

However, remember that a time series can also be autocorrelated, i.e. a signal for a particular time period can be correlated with the one previous. So, correlation is not necessarily time independent as you have said.

When you say one signal is delayed relative to the other, you are referring to the time period for which one signal is expected to follow another. e.g. during a thunderstorm, you will first see light and then hear thunder X seconds later. However, cross-correlation of a signal does not necessarily imply Granger Causality, i.e. that one causes the other, so this would still have to be investigated separately: Cross Correlation Does Not Imply Granger Causation

Your question is somewhat broad, but hopefully this clears up some of the main points for you.

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  • $\begingroup$ thanks for the reply. Really what I am trying to get clear in my head is the difference between the following terms: correlation, cross correlation and equal time cross correlation. I previously asked a question here but haven't received any feedback. I thought by breaking the question into more manageable parts I could get a quicker response. I'm clear on correlation between vars and autocorrelation for a signal with itself separated by an interval. $\endgroup$
    – TheGoat
    Mar 20, 2017 at 20:49
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    $\begingroup$ A correlation figure is bounded by -1 and +1. A cross correlation figure is not, because the purpose of this metric is to investigate the point - or maximum at which two variables are most similar, and if this is different from zero then you can deduce that there is a lag. Another answer on StackOverflow explains the difference quite well, and you might find it useful: stackoverflow.com/questions/6284676/… $\endgroup$
    – Michael Grogan
    Mar 20, 2017 at 21:05

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