The question is whether the current P/E impacts (long term) future returns. I think it does. Robert Shiller thinks it does (or at least the cyclically adjusted P/E).

Having a data point per month is not unreasonable. Prices and earnings move. The 20 year period for a 10 year return horizon is clearly too short. I'd like to see the same data over longer periods.

Prices move, but the move from month 0 to month 12 is highly dependent on the move from month 1 to month 13. It's statistical nonsense to treat them as independent variables in a regression model. You could use any biased random walk as your price series with this approach and get a correlation p value of 0.00001.

If month 1 was the crash then 0 to 12 and 1 to 13 look very different. No?

Aren't you basically saying your precise entry point to a 10 year period doesn't matter, e.g. if you enter at year zero or year 2, or January vs May in year zero? But clearly it matters a lot because the market can make huge moves in short periods.

In other words, you're saying to look at 10 year returns we should just take each decade on its own with no overlap? Clearly if I pick 1970-1980, 1980-1990, 1990-2000, or pick 1975-1985, 1985-1995, 1995-2005 I'm gonna end up with very very different results? And sure, at some point the overlap becomes too fine. But saying that 2 decades is just 2 data points doesn't sound right either?

I definitely would like to see an analysis over a much longer horizon, that'd be a more significant result.

EDIT: Totally agree the points are not independent. But it feels like there's still residual value (which I can't quite put in mathematical terms) from this "moving window".