ABSTRACT
Let {Xn, n ε N} be generated by a polynomial trend model with integrated moving average errors. It is assumed that the intercept of the model is μ up to time instant ν and it is μ + δ at ν and remains constant thereafter, where ν is an N-valued random variable (see Eq. (1.1Equation1) below). All parameters of the model are assumed to be known. Suppose {Xn } is observed sequentially and the objective is to declare the occurrence of the change quickly. It is shown in this paper that the sequential change-point detection rule N, which is optimal in the sense of minimising E(N −ν)+ in the class of rules, whose false-alarm probability is bounded by a preassigned value, is the Bayes rule of Shiryaev.
ACKNOWLEDGMENT
The second author wishes to thank Bangalore University for facilitating a visit during his sabbatical leave from the University of Madras during which period this work was completed.