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I am doing analysis of time series of returns on various currency pairs, commodities and stocks in Python/R and I would like to compare the strength of cointegration and correlation (Spearman's) between the various assets.

Basically I would like to show quantitatively that those two differ and how much for the corresponding assets. To my knowledge I have not seen a cointegration measure of strength that would allow me to do so. The only idea I have had was the significance of the cointegration test, but I do not know how I would then compare it to the correlation.

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    $\begingroup$ Returns are typically I(0) to begin with, so there is no place for cointegration among returns (but there is among prices). $\endgroup$
    – Richard Hardy
    Commented Sep 25, 2016 at 10:33
  • $\begingroup$ Yes, sorry. I have not made myself clear. That is what I meant. $\endgroup$
    – Vladimir
    Commented Sep 25, 2016 at 14:03

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Correlation can be strong or weak, and this is reflected by the location of its absolute value in the range between zero and one (close to zero - weak, close to one - strong).

Cointegration is a yes/no phenomenon. Either it exists or it does not. Either there is a linear combination of integrated variables that has a lower order of integration, or not. You cannot quantify its strength.
The significance of cointegration test measures the confidence with which you can make statements about presence/absence of cointegration; but that is not quite the same as measuring the strength of cointegration.
What you could probably do as an alternative is examine how fast/intensive the error correction mechanism works (how fast the gap from the equilibrium closes).

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