Redundancy helps. Use multiple analysis methods, show someone else your results, etc. If everything turns out the way it's supposed to, then that's strong evidence that the correlation is "real".
EDIT: It appears I've been ninja'd. Yes, I am not using the term "correlation" in the technical sense, but in the colloquial sense of "any dependency". Sorry if that's been making things unclear.
I still don't understand in which sense do you use the word "real" in 'correlation is "real"'.
Let's say you have two time series 100 data points in length each. You calculate their correlation, say, Pearson's correlation. It's a number. In which sense can that number be "real" or "not real"?
Do you implicitly have in mind the sampling theory where what you observe is a sample estimate and what's "real" is the true parameter of the unobserved underlying process? In this case there is a very large body of res...
Another month, another rationality quotes thread. The rules are: