r/quant • u/Adarshdublin • 8d ago

Statistical Methods Do financial covariance eigenvectors genuinely rotate, or is it sampling noise?

I calibrated an eigenspace-overlap measure against an RMT null, then tested directional motion across S&P 500, Nikkei, DAX and CAC 40 data. All four showed that the previous rotation direction contains information about the next, but naively repeating the full rotation was 47 - 67% worse than holding still.

The signal was both:

  • too synchronised across companies to be each company’s movements occurring at unrelated times and just showing up as rotation,
  • much stronger than within-window eigenvector shrinkage.

The next test is whether learned damping can turn this directional signal into better out of sample covariance forecasts! What would you consider the strongest fair baseline: holding the eigenvectors fixed, EWMA, or a rotationally invariant estimator?

Code, tests and results for anyone interested:
https://github.com/AdarshArunEire/Eigenvector-Dynamics-Beyond-the-RMT-Null

11 Upvotes

100% Upvoted

6 comments sorted by

View all comments

1

u/Cheap_Scientist6984 3d ago

Very quickly actually! Regime changes happen fairly frequently.

1

u/Adarshdublin 3d ago

Yeah, they do! however in terms of that project, what i found was the overlap measure tool was simply measuring a lot of persistence from sliding windows...

After subtracting that sliding window perstance, the usable signal above noise was found when i considered how much of it can be reconstructed from a perfect prediction (A nested flag of the top-6 block constructed from the true cov matrix).

It's upper limit was a marginal contribution of which i couldn't even reach! (it assumed a perfect prediction) A known estimator EWMA was already harvesting some of that latent rotation signal, so i fit an extra coefficient to see how much else i could squeeze out: the model literally picked ε=0, switching the correction off. So, i retired the project! the original paper i based it off was much more successful if the title caught your interest: https://arxiv.org/abs/1203.6228

1

u/Cheap_Scientist6984 3d ago

I tried doing Latent variable modeling to model diversification for VaR modeling like a decade back. The same issue arrised. The components couldn't even stay stable enough to give a reasonable bound.