A direct answer to your question:
Noise trading as an explanation for the outliers was my idea. ChatGPT help make my idea more readable.
The possibility of non-linearity is obvious and no one should need a LLM to consider that as a possibility.
As I recall, I was discussing homoskedasticity in a different context earlier this morning — with ChatGPT, actually — as I was working to improve one of my own models. So it was already top of mind when I made the post.
I originated the idea of improving my linear models with inverse-volatility weighting. It’s not really a new or particular advanced idea for linear regressions. But sometimes ChatGPT helps me with ideas like that while–at times–the ideas are new or forgotten in the forum.
But also — I’ve checked for homoskedasticity in P123 data in the past. It’s been a while, but what I found is that many of the features we rely on are nowhere close to homoskedastic.
We’re likely violating this assumption for most features, and this isn’t new — it just tends to get forgotten.
I addressed heteroskedasticity in a forum post years ago — well before the rise of LLMs. It’s one of those issues that seems to get recycled, over and over, with no memory in the forum. Ranking and market timing in combination for stock forecasting models - #10 by Jrinne
I was implementing a version of inverse-variance weighting this morning for an AI model. Not sure I can help you with an Excel version of that. But pretty simple in Python.
Here is a link that may be helpful: Solving the problem of heteroscedasticity through weighted regression
Also Wikipedia: Weighted least squares
Regardless, it is worth looking at some of our assumptions for P123’s AI in my opinion.
This is strong empirical work — but to get published in a peer-reviewed journal, you’d likely need to explicitly address outliers, model assumptions, and heteroskedasticity. That’s especially true when you’re evaluating something as foundational (and widely defended) as CAPM.
In a thread discussing the academic use of P123, I think this is a serious contribution to the topic