New to statistics here, so please bare with me if my terminology is incorrect.

So I know that you can use the Pearson Correlation Coefficient to work out the strength of the correlation of a set of data points and whether it's going up or down.

Is there any method for me to compare the correlation behind two lines?

So for example, say I have two sets of data (eg. maybe one is no. of murders per year and other is no. of DVDs sold in the US) and I have data for these datasets over many points in time (although not guaranteed that the two datasets have data collected at the same exact point).

If I use date as the x axis , I can draw a line for each of these data sets to see what happens to them over time. How do I measure whether there is a correlation between these two lines? Take into account that the lines may not move in a linear rate.