Does it really matter if a correlation is spurious? Let’s say you are trying to find if there is a correlation between two stock prices, where both are likely non stationary series. You have no concern as it relates to a potentially causal relationship...
You run a simple correlation analysis against all the rules. Both our series are autocorrelated and non stationary. You find there is a 98% correlation so you conclude they depend on each other.
This is the conversation I just had with a colleague... but I think they are 100% wrong and I’d like some confirmation.
If you find two autocorrelated and non stationary series to be 98% correlated, then the correlation is likely spurious. What this means to me is that the correlation we observe is likely due to complete chance (and their correlation is likely a result of their mutual dependence on something else outside of the two series themselves). So if our goal is to identify the extent to which these two series “depend” on each other, finding a valid correlation coefficient is necessary. Is this correct?

The problem with spurious relationships - in the narrow context of pair trading - is not even with causality. The problem is that the relationship doesn't hold out of sample. This means that when you actually start trading on the developed algorithm, you won't make any money. And that can be a little bit of an issue, right?
