I have a time series that I am trying to analyze. There are two sequences in the series that appear to be very similar and I want to determine if that can be logically inferred, and if so, what does that tell me about the series.

It is my understanding that one must be very careful about assuming patterns in time series are not random, and that statistics provides a number of tools to rigorously make such determinations. I hope to enlist the expertise of the pros on this forum to help guide me through this process.

Since my understanding of statistics is very limited, I would like to work through this analysis in a methodical manner so that I can assimilate each step, and I would greatly appreciate your indulgence if my progress seems too plodding.

The series I am studying has over 30k points. It does not appear to be stationary -- having both trend and possible cyclic characteristics -- and it is not normally distributed.

The two sequences of the series I am interested in are only a few hundred points in length each.

The cumulative percent change from point zero (the peak) of the overlaid sequences looks like this:

Is there a correct or best way to quantify the similarities between these sequences?