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/