This correspondence concerns problems of time-series forecasting under
the weakest of assumptions. Related results are surveyed and are poin
ts of departure for the developments here, some of which are new and o
thers ape new derivations of previous findings. The contributions in t
his study are all negative, showing that various plausible prediction
problems are unsolvable, or in other cases, are not solvable by predic
tors which are known to be consistent when mixing conditions hold.