I am trying to develop a logic to identify association between different time series for association mining. I have a lot of series and need to find whether or not the association exists. I figured two ways to do this:


Constructive: try to find relation in given two series.
Destructive: try to prove that relation does not exist.


Are there any existing mathematical parameters to identify such relations? if not, any suggestions?

In a sense, the mean is used because it is sensitive to the data.  If the distribution happens to be symmetric and the tails are about like the normal distribution, the mean is a very efficient summary of central tendency.  The median, while being robust and well-defined for any continuous distribution, is only $\frac{2}{\pi}$ as efficient as the mean if the data happened to come from a normal distribution.  It is this relative inefficiency of the median that keeps us from using it even more than we do.  The relative inefficiency translates into a minor absolute inefficiency as the sample size gets large, so for large $n$ we can be more guilt-free about using the median.

It is interesting to note that for a measure of variation (spread, dispersion), there is a very robust estimator that is 0.98 as efficient as the standard deviation, namely Gini's mean difference.  This is the mean absolute difference between any two observations. [You have to multiply the sample standard deviation by a constant to estimate the same quantity estimated by Gini's mean difference.]   An efficient measure of central tendency is the Hodges-Lehmann estimator, i.e., the median of all pairwise means.  We would use it more if its interpretation were simpler.
