Actually, this is not correct. Any proposal for market timing requires an observable x[t] that is correlated to R[t+d] for d>0. The returns may themselves lac

Actually, this is not correct. Any proposal for market timing requires an observable x[t] that is correlated to R[t+d] for d>0. The returns may themselves lack any auto-correlation. If market returns are auto-correlated in some way, then x[t] could be a function of R[s] for s<=t. In the context of this game, x[t] would be some information about the internal state of the RNG at time t.