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I suspect that you are mixing correlation and cointegration. What you describe as the co-movement of prices sounds like cointegration.


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Actually prices dont make sense as they are correlated with previous samples (prices), returns are not. Better will be difference between prices, but then you dont have reference point and comparability between assets, so eventually you need returns. At the end that is what you are interested in I think as profit is usually measured in return.



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