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Arnold: your posts on this sort of topic always make for depressing reading. Especially since I know you actually have experience with this stuff (I don't).
So, it's worse than I thought.
The model is Y(t)=R(X(t)).
I assumed they were putting a curvy ruler on X(t) to forecast X(t+1), then plugging that into the model to forecast Y(t+1).
But from what you are saying, I can only conclude that what they are really doing is putting a curvy ruler on Y(t) to forecast Y(t+1), then using the inverse of the model to forecast X(t+1), and then pretending to work backwards again, and use the model to forecast Y(t+1). In other words, the model is only there for show. That's the only way to make sense of the observation that they do better at forecasting Y(t+1) than they would if they actually knew X(t+1).