# Statistically describing/visualizing "non-overlap" in a large set of time-series data

Extensive edit of the original question while I've been able to refine my thoughts and write some better code.

Consider data from two processes, each with can produce many, many time series curves that will have lots of overlap in their results. An example image is below, using relatively few curves - the actual application has many thousands for each process whereas this only has 250 each (Red vs. Blue):

There will be a large amount of overlap between the two, but for example the "Red" process is the only one that can produce very high, very sharp peaks early on, whereas "Blue" seems to produce higher peaks in the X = 3000 to 4000ish range, etc. What I'm looking for is a way to statistically quantify or visualize that non-overlapping space where there's lots of overlap.

Anyone have any ideas? One thing I've considered doing is ignoring that these are time-series, and generating something like a kernel density for each and subtracting one from the other - areas far from zero would then be places of less overlap, but I'm not sure how defensible that is.

The actual application of this is a series of parameter searches for a dynamical system - essentially, the intent is to produce many, many numerical results of a system of differential equations using two different approaches, and then find anywhere in the results where, for example "Red can generate results with this value, whereas Blue cannot" when for the most part some parameter value for Red will provide the same results as a different parameter for Blue.

• It would help to provide a precise, quantitative definition of what you mean by "overlap." (I can think of many different interpretations in your time series context.)
– whuber
Jan 23, 2013 at 18:24
• The difference between the two distributions is indistinguishable because the variance of the series swamps any visible difference in the central tendency. A solution then is to approximate the plot the approximated distribution in the chart (most likley via some running, smooth estimate of the series). Examples can be found at Preferred methods for graphing time-series data to present “averages”? and Show series of exponential decay distributions in one chart. Jan 23, 2013 at 18:58
• This advice seems general enough to extend to however you want to characterize "overlap" - but some specific aesthetic qualities to display overlapping bands is to use strongly diverging colors and transparency judiciously (and only have a max of two groups in any one plot). Jan 23, 2013 at 19:00
• @whuber See the edit, if that helps at all? Jan 23, 2013 at 19:15