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Which correlation coefficient is the most appropriate to compare 2 time series? I want to compare the variation of one variable for 2 regions, have regional data for the last 30 years. Is Pearson correlation ok or should I rely on Kendall's tau b or Spearman's rho and why? I tried to google it and analyse what I found, but I'm still not sure.

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    $\begingroup$ I'm no expert in time series, but browsing our related threads might bring useful information. $\endgroup$ – chl Jan 2 '14 at 21:33
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    $\begingroup$ looks very similar to this question: stats.stackexchange.com/questions/80577/… $\endgroup$ – forecaster Jan 2 '14 at 21:44
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    $\begingroup$ and this question, and this, and this, and this... $\endgroup$ – Nick Stauner Jan 2 '14 at 21:58
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    $\begingroup$ the 3rd & 4th threads I linked explain some differences among the 3 correlation estimators that you mentioned specifically, but they mainly differ in what kinds of data they best address in other terms (continuous vs. ordinal, normally distributed vs. nonparametric). they don't take into account temporal contiguity across your individual time series of observations, so a method that would might be preferable, depending on what exactly you want to estimate. you should probably be more specific about that if you can; it's impossible to see how your question is different from others as written. $\endgroup$ – Nick Stauner Jan 2 '14 at 23:38
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    $\begingroup$ If, after considering some more sophisticated methods of comparing time series, you agree that Pearson's $r$ isn't appropriate to your analysis, Kendall's $\tau$ and Spearman's $\rho$ aren't likely to be much better. You may need to reformulate your question in that case, because you wouldn't just be talking about a simple correlation, I suspect. $\endgroup$ – Nick Stauner Jan 2 '14 at 23:41
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For time series some version of Pearson correlation is most used, in the form of the autocorrelation function (for one series, correlated with itself at various lags) and the cross-correlation function (for two series) likewise. They are correct when all conditional expectation are linear.

If you suspect that may not be the case, you should start with some visualization of the two series! I have not seen any detailed descriptive analysis of two time series, that would be rather interesting ... In R you could play with the function coplot and you could make scatterplot matrices, replacing what would be one number in each of the two functions above (autocorrelation, crosscorrelation) with a scatterplot. You could also look into copulas used with time series.

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