Avoiding a common mistake with time series

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Um caso em q a tendência mascara o resto da série criando correlações elevadas

A basic mantra in statistics and data science is correlation is not causation, meaning that just because two things appear to be related to each other doesn’t mean that one causes the other. This is a lesson worth learning.

If you work with data, throughout your career you’ll probably have to re-learn it several times. But you often see the principle demonstrated with a graph like this:

Dow Jones vs. Jennifer Lawrence

One line is something like a stock market index, and the other is an (almost certainly) unrelated time series like “Number of times Jennifer Lawrence is mentioned in the media.” The lines look amusingly similar. There is usually a statement like: “Correlation = 0.86”.  Recall that a correlation coefficient is between +1 (a perfect linear relationship) and -1 (perfectly inversely related), with zero meaning no linear relationship at all.  0.86 is a high value, demonstrating that the statistical relationship of the two time series is strong.

The correlation passes a statistical test. This is a great example of mistaking correlation for causality, right? Well, no, not really: it’s actually a time series problem analyzed poorly, and a mistake that could have been avoided. You never should have seen this correlation in the first place.

The more basic problem is that the author is comparing two trended time series. The rest of this post will explain what that means, why it’s bad, and how you can avoid it fairly simply. If any of your data involves samples taken over time, and you’re exploring relationships between the series, you’ll want to read on.


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