As you suggest, it's not always incorrect to shift and rescale data for visualisation. In fact, that is exactly what a linear correlation calculation does: the

As you suggest, it's not always incorrect to shift and rescale data for visualisation. In fact, that is exactly what a linear correlation calculation does: the data is shifted to have mean zero and rescaled to have variance one, then the covariance is computed. The real problem is that often, the two timeseries being compared are too simple to demonstrate whether there is a relationship present. If they're both essentially straight lines as in the Butcher's Dog graphs, you may see a spurious relationship. What you need -- in unscientific terms -- is to see one timeseries do something weird, and the other timeseries reacting to the weird thing in a manner that fits the narrative. Straight lines don't really do that, but often the first difference of two timeseries that look like a straight line will be good enough.