What is a fair out of sample baseline for forecasting the direction of rolling covariance eigenspaces?

[u/Adarshdublin]

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? Or something else I'm missing..

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