Say I have $n$ pairs of time series data. For each pair, I calculate a measurement which looks at the overlapping fraction of each time series pair, resulting in $n$ overlap values.
EDIT : I define "overlap" of the time series as follows. For each time series pair, divide one signal by the other (the signals are the same length), resulting in a new signal $d$. Then, given some threshold $x$, look for each instant in time that satisfies $1-x <= d <= 1+x$. Whenever this condition is satisfied, say that the signals are "overlapping". The variable $x$ is a tolerance threshold allowing us to change how close the signals get before we accept them as overlapped (if $d=1$ then the signals are perfectly overlapping at that time instant). The final statistic used tells us the fraction of $d$ that the signals are overlapping - according to the above definition - i.e. it tells us how much (relative) time the signals in each pair are overlapped. It is the distribution of these values that I am interested in.
I would like to determine if the distribution of the overlap values is non-random, i.e. if my time series pairs were somehow randomized, would the distribution of these "random" overlaps be different from the distribution of the "real" overlaps I have already calculated.
Any help would be much appreciated.