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I'm looking for a robust metric to express the similarity between two time series having the same behavior, as simplified below. When one increases, the other increases (same for decreasing or being flat). Their relative proportionality is not constant over time. The Spearman coefficient works well for noise free signal, but fails to capture the similarity when there is little noise. The Pearson coefficient is too low. What metric could I use ? Ideally, the metric should also indicate strong correlation for two signal being both "flat" (i.e, with no significant increase or decrease).

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  • $\begingroup$ Please see the approach outlined in this post: dsp.stackexchange.com/questions/75993/… The issue is similar in that you want to determine similarity with equal weight to any representation at a given time, so you want equal weight if the answer is 0 (flat) or the answer is 1000. For that map your symbols to orthogonal symbols with equal weight. The bins of an FFT is one set that can have any number of symbols that you need. $\endgroup$ Jul 5 '21 at 15:44

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