Discrimination Between B-Processes is Impossible

Two series of binary observations x ₁,x ₁,… and y ₁,y ₂,… are presented: x _n and y _n are given at each time n∈ℕ. It is assumed that the sequences are generated independently of each other by two B-processes. The question of interest is whether the sequences represent a typical realization of two different processes or of the same one. It is demonstrated that this is impossible to decide, in the sense that every discrimination procedure is bound to err with non-negligible frequency when presented with sequences from some B-processes. This contrasts with earlier positive results on B-processes, in particular, those showing that there are consistent `(d)]\bar{d} -distance estimates for this class of processes, and on ergodic processes, in particular, those establishing consistent change point estimates.