This question relates to Financial Machine Learning, and more specifically to competitions like Numerai.
In this competition we have a dataset X and a target y (return over a given horizon). The dataset contains some features (say feature_0 to feature_n) and time. Different stocks are available each time.
One important metric is the correlation bewteen features and the target. Correlation can be either spearman or pearson. We can observe past correlations. I was wondering if there is a standard way to model this kind of correlation over time.
The correlations seems very random, changing signs quite often, oscillating around 0. I was thinking about some mean reverting process, centered at some value near 0. I was thinking about an OU process with a small drift and a high reversion coefficient.
However, as they are correlations, they would be capped by -1 / +1. I don't know how to deal with this. As the correlation are oscillating around 0, I am tempted to ignore this constraint. But it might be better to add some logistic function somewhere.
Any idea of a standard approach to model correlation over time ?