About the problem of interest rate forecasting I find various paper that address the problem from the perspective of risk premia and affine term structure model. For example Cochrane and Piazzesi (2005), see here: https://www.aeaweb.org/articles?id=10.1257/0002828053828581
In particular the forecast is about excess return, excess respect to short term rate in zero curve setting. However in real world, at least in my experience, fixed income traders work directly with bond yield and not with zero curve, and see directly the observed yield and not some "excess measure".
I know pretty well that bond price is mathematically related to bond yield and that, therefore, diff yield is related to bond return. However I don't know if predictability of some excess return in zero curve setting imply necessarily predictability of bond (diff) yield. Informally speaking it seems so but ... formally? Have you some proof? I looked for but never never find it.