I want to test the correlation between various timeseries. As far as I can tell, finding the Pearson correlation coefficient is a good way to do this.

The results I get, however, are not entirely in agreement with my intuition (which I realise they don't have to be :).

In the plot attached, I would say that (in the work I'm doing), the two timeseries are really well correlated; the local minima and maxima occur at pretty much the same time (with a little variation added in).

The correlation coefficient (0.37) is not very high though. I can understand why this is - sometimes a local maximum may only have a small peak, when the other series has a large peak, or they might be offset in time at some pointsenter image description here etc..

Is there a more appropriate test available that would be more in tune with my intuition that these series seem to go up and down pretty much in synchronisation?

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    $\begingroup$ Has your question already been answered here or here? $\endgroup$ – MånsT Apr 22 '15 at 10:20
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    $\begingroup$ An outcome such as 0.37 should be judged in some context I think. In itself 0.37 can be a respectable correlation. The plot you show does not look like a striking example of synchronisation to me, for the reasons that you mention (amplitude differences and local offsets), so 0.37 seems about right. How about constructing a model suitable for your application that allows you to create an empirical distribution of correlations for time series that represent a'background level' of correlation? $\endgroup$ – micans Apr 22 '15 at 11:51
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    $\begingroup$ Not quite your question, but as you realise a correlation is not "seeing" the data as you see it on a time series graph. Always looking at the corresponding scatter plot will make it clearer what a correlation is (and equally crucially is not) responding to: it won't offset for you unless you look at lags. By and large, the issue is not which measure to use, but which model for the data produces the best match. Here we see just two time series, and you need substantive knowledge to know which way to proceed, principally whether there is some causal relation or mechanism linking the two. $\endgroup$ – Nick Cox Apr 22 '15 at 12:03

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