Zeelotes beat this subject to death some time ago.

I think he concluded that a "what's working lately" (WWL) approach works best looking at more data and switching less often. A few years, IIRC. But at the time almost all screens were considered only 4 or 5 deep, so you need a lot of data to get any statistical support at all.

Perhaps that lookback would be shorter if you're using extremely deep, and markedly different, screens so that there is some statistical support to your measurement.
e.g., if you're running a 40 stock dividend portfolio or a 40 stock no-dividend growth/momentum portfolio, maybe a short lookback makes sense?

A random example of that effect comparing broad and different portfolios.
Compare the relative performance in the last 3 months of a portfolio of all dividend payers, and of the S&P 500.
If the dividend payers did best, then in the next month, a portfolio of the highest half of dividend payers does 15%/year better than it does when the S&P did best in the prior 3 months.
This is sort of a slow-motion minimal version of Zee's speculative/defensive signal.
If you used that as a signal, checking once per month and going with hidivs or SPY, you'd switch horses 2.7 times a year (1.35 round trips to SPYland) in theory beating the S&P by several percent a year before friction. over 7% in my quick test which was monthly starts only over 38 years.

As for statistical noise, I once created a rule of thumb that 4000/([number of trade dates in a test]*[number of picks in the screen]) will get you the error bar size on the CAGR you measure.
e.g., a 10 stock screen monthly for 10 years would be 4000/(10*120) would be plus or minus 3.3% measurement error as a crude estimate, assuming reasonable turnover. Worse for a screen with low turnover.

Jim