Test to use for series comparison

#1
I have a silly example to illustrate something that I am looking into, but I don't want to give up what I'm after just yet. So indulge the stupidity of the question for a moment...

I have two hypothetical time series: one for the monthly rainfall in New York City, and one for the monthly Purchasing Manager's Index (PMI: an economic indicator). There are some 50 years of data for each.

I wish to determine if there is any correlation between the two. What test should I use?

Please phrase the question for a statistical simpleton. Or... is that a simpleton at statistics....?
 
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