How to find the offset between two time series that minimizes their euclidean distance?

Question

I'm looking for some methods to compute shape similarity between two curve segments.

I have two time series x1 (purple line) and x2 (red line) and I would like to find the y-offset that minimizes the difference between the two curves (the sum of the square differences), and use this difference as a similarity measure.

How can I find this offset?

Answer 1

After a relaxing week end, it's easier to see the obvious: it's the average distance between simultaneous points of the data sets.