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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.

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Despite the rather unconventional terminology used I would say you are pretty much spot on with what you are doing and what you try to achieve. I would, however use log returns in order to get an identical percentage no matter whether you measure the distance from 100 -> 90 or 90 -> 100, for example. You can also standardize the value you capture by differencing the observed distance and mean distance and then divide the difference by the observed standard deviation of the distances over a specified amount of data points, similar to z-value. That gives you the difference in terms of standard deviations.

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I like the Z-score idea; that should solve a lot of the OP's issues with magnitude. –  chrisaycock Dec 18 '12 at 1:21
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