I didn't see any of the experiments you did as an invalidation of CAPE.
I'd like to be as clear as possible, I'm not claiming to have invalidated CAPE.
CAPE "works" in the sense that there's good prediction accuracy of long-terms returns (but the predictive accuracy depends on what period of time you're looking at, as I showed).

What is invalidated, at least in my mind, is the logic chain:
(1) because CAPE "works" (good accuracy), and
(2) because CAPE is a valuation measure
then "CAPE working" is a long sought demonstration that "valuation works".
I'm sure I'm not the only one who had subscribed to that logic chain, given the huge number of publications on CAPE, and on what its value might imply for the economy.

> smoothing earnings takes out a lot of the volatility to begin with
Shiller set out to smooth earnings, not eliminate earnings.
But I took out in FAPE1 all the volatility, every single wiggle of earnings, so that there's basically no information left about earnings other than two numbers, slope and intercept (you can even change those two numbers by a large amount), and FAPE1 still achieves basically the accuracy of CAPE.
FAPE2 doesn't even use earnings at all, yet it still looks like (graph) and feels like (accuracy) CAPE.

To my mind, a valuation measure that walks up to you and says
"I'll compare price to earnings for you and predict the future"
but the predictions don't really depend much on earnings (if at all on earnings, at least explicitly), isn't doing much valuation. That's disappointing!