I have a few time series of models to analyse in terms of how far/close they are to their underlying limit. The limit is a simple value on the y-axis (always positive), and the series can act arbitrary with respect to that - it can be negative for most of the time, then jump up and oscillate, or stay close under the limit, or even break the limit a couple of times... My question is how to best capture the "closeness" of the time series?
My current idea is as follows: for each data point we calculate distance = (limit - curr_value)/limit. This can be very big, if the values are negative (far from limit), close to zero and negative if breaching. I would then compute a weighted average of all values.
Does this make sense at all, or perhaps a different strategy should be used? Thanks a lot for your opinions.