It looks as if there is a lot of compensating corrections going on in that algorithm. I can sense that because the forecast always seems to be lagging, sometimes ever-so-slightly, from the actual curve. And in places that it makes a sudden lurch away from the actual, it gets brought back in-line quickly.

So you are saying the information content is limited to just a few near-neighbors, and that defines how far you can forecast into the future?

I am still subscribing to the saying that you can't get something from nothing. So, without understanding anything about the underlying algorithm, it appears that these curves are very similar to continuously updated estimators, such as embodied by Kalman filters. These do work well for short-term forecasting, such as navigation control systems, but how far in advance can they really forecast?