What level of correlation coefficient suggests correlation?
One way to look at it is that $r^2$ (yes, I do mean $r^2$, not $r$ or $|r|$) is the fraction of the variance of the target (the series A) that is explained by the estimator (a linear function $\alpha + \beta B$ of the series B).  Note that if Series A had variance $\sigma^2$, then the variance of $(A - (\alpha + \beta B))^2$ (what B cannot explain about A) is $(1-r^2)\sigma^2$.  So, if $|r| &lt; \frac{1}{\sqrt{2}} \approx 0.707\ldots$, less than half the variance has been explained, and so one viewpoint is that a correlation of less than $70\%$ or so suggests that the linear estimator being considered here is not all that great.