A Time Series Analysis of Binary Data

Abstract

Binary data d 1 , d 2 , …, d n are assumed to be generated by an underlying real-valued, strictly stationary process, { X k }, and a response function F. For a given monotone nondecreasing function F from R to [0, 1], D k takes on 1 with probability F ( x k ) and 0 with probability 1 - F ( x k ), where X k = x k . It is shown that all strictly stationary binary processes are characterized by such a procedure. Several approximations to the n -dimensional joint probabilities of D k are developed when X k is a Gaussian first-order autoregressive process. Model-building procedures and methods by which to estimate parameters of a given model are discussed. The predictor of d n + 1 that minimizes probability of error among all randomized rules is determined and for certain cases a bound for this probability is found.