Binary datad1,d2, …,dnare assumed to be generated by an underlying real-valued, strictly stationary process, {Xk}, and a response functionF.For a given monotone nondecreasing functionFfromRto [0, 1],Dktakes on 1 with probabilityF(xk) and 0 with probability 1 -F(xk), whereXk= xk.It is shown that all strictly stationary binary processes are characterized by such a procedure. Several approximations to then-dimensional joint probabilities ofDkare developed whenXkis a Gaussian first-order autoregressive process. Model-building procedures and methods by which to estimate parameters of a given model are discussed. The predictor ofdn+ 1that minimizes probability of error among all randomized rules is determined and for certain cases a bound for this probability is found.