If you're seeing trends in your residuals that's a violation of the independence assumption of linear models (assuming you're using about a linear model since you're talking about "linear predictions").

I'm in a different field but an arbitrary 27 years (1998-2024) of data and the autocorrelation both would get flagged in a review for me. Not to give statistics homework but you should test and correct the autocorrelation issue you're describing in the model and if the data goes farther back I would go farther back, too (with how you're describing the errors going off pattern then back on it sounds like the inference here would be at least somewhat unstable depending on year chosen).

Edit: these are the assumptions and basics of how to correct for violations, in particular you're describing a violation of assumption 2 but you should test for all of them - https://www.statology.org/linear-regression-assumptions/

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tdb7893 11 hours ago | parent [-]

I was checking if there was a response and upon reading your comments again, looks like your method is less a model and more just some ad hoc procedure. Based on what your conclusion is it sounds like a linear model based on demographic data would work and linear models are easy to train. Though by your summary there are probably going to be issues with the model and you have the same issues with your procedure, you just can't tell because it hasn't been rigorously specified.

There's a channel on YouTube called Statquest that teaches statistics in a pretty accessible way if you're interested in analyzing this sort of data.

	▲	romaaeterna 6 hours ago \| parent [-]
		I learned my statistics in university, not Youtube. You are confusing yourself about residuals. To make my point in the original post, I held the group scores fixed and extrapolated combined scores based on changing population sizes. This is straightforward. Simple even. \(\widehat S=\sum_g p_gS_g,\) Why did I call this "linear"? (Not a "linear model", your term, because it is not). The model function actually tracks the population function. Over the 25-year period, however, this trend is in fact linear because the White-to-Hispanic population trend is linear on that timescale. Over a longer timescale it would not be.