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By correlation coefficient, I am referring to Pearson product-moment correlation coefficient here.

We all know that correlation doesn't imply causation, but does high correlation coefficient mean anything? The reason I ask this is that if one looks hard enough, one can find all sorts of correlation between any set of data in stock market ("torture the data until it confesses"), so I now think that high correlation coefficient doesn't mean anything at all.

Except for the situation whereby we can trace the causation between two matters, is there any other situation whereby high correlation coefficient means anything?

Take a specific example, if I see that stock A and stock B have a perfect correlation coefficient ( after extensive data mining) and I can't find out the reason why, or any causation between them, and when stock A rises, should I conclude (with high percentage of confidence level) that stock B will also rise? As far as stock B is concerned, what inference I can draw from the rise or fall of Stock A price?

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  • $\begingroup$ It seems that you are all after a reliable indicator of causality (only this "makes sense"). Correlation isn't necessarily causation, causation is always correlation. What if causation do not exist out there at all and is simply a way we verbalize/interpret some correlations some time? $\endgroup$ – ttnphns Apr 11 '14 at 8:30
  • $\begingroup$ @ttnphns, I am not too sure your comment has anything to do with my question. is it that you find my question is unclear? $\endgroup$ – Graviton Apr 11 '14 at 8:37
  • $\begingroup$ My comment was in no way an answer and is only partly relevant to your entire question; my comment clearly implies: correlation always means something. Unless you ignore it. $\endgroup$ – ttnphns Apr 11 '14 at 8:41
  • $\begingroup$ @ttnphns, I don't think so;correlation doesn't always mean anything, have you heard of the phrase "torture the data long enough until it confesses"? $\endgroup$ – Graviton Apr 11 '14 at 9:47
  • $\begingroup$ The phrase has nothing to do with my comment. $\endgroup$ – ttnphns Apr 11 '14 at 10:22
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You seem to be conflating two thing:

1) What does correlation mean?

2) Can data mining and other issues mess this up?

Correlation between two variables means that the two variables are correlated: One tends to be higher when the other is higher and lower when the other is lower. Correlation may be due to some third variable, or it may not. It may be due to an outlier, or it may not, etc.

Correlation of time series (like your two stocks) is often due to a 3rd variable: Time. Stock prices tend to move in sync with each other.

And, if you "extensively data mine" then even random noise will produce some very strong correlations. If you look at, say, the correlations of 1000 stocks with each other, then you have 1000*999/500 correlations. You can see how many would be (say) above .9, even if all the prices were utterly from knowledge of the correlation coefficient's properties (standard error) or from simulation.

But if you look at those 500,000 correlations, you will see that they don't behave exactly like the random ones: they tend to be positive.

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    $\begingroup$ The popularity of expressions like "correlation does not mean causation" may lie in affection for alliteration and assonance. Why pick on correlation? It's no worse than many other methods. There are shelves full of books on causation, so the question can't be decided briefly, but I'd venture riskily that causation is mostly outside statistics. Nevertheless statistics can throw some light on causation, if only by underlining which relationships are broadly consistent with a causal idea, and which not so. That does usually work better with a model, which correlation doesn't provide. $\endgroup$ – Nick Cox Apr 11 '14 at 13:37
  • $\begingroup$ Peter, you are saying that random noise can produce very strong correlations, so that means that it is wrong to infer that there must be some relationship between two variables, even though they are highly correlated? $\endgroup$ – Graviton Apr 14 '14 at 5:56
  • $\begingroup$ We can't say there must be a relationship in a population from any thing we find from a sample. All we can do is estimate how strong it is and estimate how good our guess is. It could be chance. You could toss a fair coin and get 10 heads in a row. $\endgroup$ – Peter Flom Apr 14 '14 at 9:30

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