To be concrete, given 2D numerical data as is shown as line plots below. There are peaks on a background average movement (with small vibrations). We want to find the values of pairs (x1, x2) if those peaks drops down to average; or (x1) only if the line doesn't back to the average.
There are thousands of such 2D data.
What is the right statistic or machine learning algorithm to find x1 and x2 above without plotting?