I was reading Nassim Taleb's Paper: Fooled by Correlation and found it very informative. I had always struggled with finding value in correlation in Finance, especially seeing a lot of bad applications in the workplace, however this paper got me thinking.
Would splitting up correlation into subsections as shown here have informative value for model building?
Say I wanted to model the % price change (or the log % price change) for a pair of assets, would it be better to look at the correlations for the downwards movements and upwards movements separately?
Are there any risks to doing so for lagged correlations between the variables?
A more general question as well, how do we prove causation in asset price relationships with different features in our model?
Also, do there exist any Python libraries that calculate these subsets of the overall correlation?