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Is there a statistical procedure that can measure the concordance between two sets of data that have, say, a sinusoidal tendency?

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short answer (the question is rather imprecise). Say $y_{1t}$ and $y_{2t}$ are your two sets, then $z_t=y_{1t}-y_{2t}$. Then it amounts to checking whether $z_t$ is bounded (in your example it will be, if you sample $y_{1}$ and $y_{2}$ over a long enough amount to time).

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