Lets say I have 2 time series that look like this for a number of different test subjects:
The lines represent values on 2 different metrics recorded at different points in time (minutes)
I have a prediction that says when the blue signal is high, the green will be low, and vice versa (i.e. they are inversely related). You can see this prediction play out between time points 1-7
I'm looking for a way to quantify the level of similarity (or I guess dissimilarity in this case) between the two signals, maybe some inferential test, to suggest that my prediction/hypothesis is correct. Are there any techniques designed for this type of analysis?
I've seen a few posts on here suggesting the use of a cross-correlation (e.g. Correlation between two time series), however, I dont think that would be useful in this case. A cross-correlation will tell me the maximum degree of similarity, and also the lag at which that similarity occurs. But I'm not really interested in similarity after time shifting because I only care about similarity as the data is recorded (lag 0)
I've tried a regular pearson correlation, but its resulting in really small correlation values. Are there any other methods that can help me determine whether my hypothesis is correct?