I have a set of companies. For each, there are two different time series of data *(equal length, same period). For example, these can be different financial indices measures every year. I want to answer the question if there is a tendency for the two series to correlate. That is, there are companies that show strong correlation and there are companies that show no correlation. I want to tell if it is more likely or unlikely that these series are correlated.
In order to unswer that question to myself, I created a distribution histogram of those correlation coefficients. From it, I see that the distribution resembles skewed normal distribution with highest point somewhere between 0 and 0.5. So, visually, I see that it more likely that the series do not correlate. I am looking for a way to express that more strictly.
My questionss are:
What methods would you use to describe the distributions of correlation coefficients?
Would you focus on the distribution of correlation coefficient at all or analyze the set in some other fashion?