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In this example, at timepoint 5, both signals move up together. I would like to quantify these similar movements, and ideally disregard the parts where the signals are almost constant. What correlation or similarity measures would be best here?

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One option is a Granger causality test which a statistical hypothesis test for determining whether one time series is useful in forecasting another. One time series is said to Granger-cause another time series if the lagged values of one times series provide statistically significant information about future values of another time series.

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This looks like a job for Dynamic Time Warping (DTW), as this algorithm calculates an optimal match between two given sequences. If you would like to implement it in Python (for example), I can recommend DTAIDistance. The documentation of this project is also very helpful if you want to understand this method in detail.

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  • $\begingroup$ But DTW would also count the constant parts as similar, wouldn't it? I would ideally like to disregard or at least give less weight to the parts where one or both are constant. $\endgroup$ – Tirtha Oct 30 '19 at 12:17

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