Estimating the Mean of a Correlated Binary Sequence with an Application to Discrete Event Simulation

This paper discusses a procedure for interval estimation of the mean @@@@ of a correlated binary (0,1) sequence. The method assumes that the sequence is strictly stationary and that a particular string of m binary digits is a recurrent event in the sequence, where m≥l is unknown. Of the 2m choices for the possible recurrent events, the strings of all zeros and of all ones are examined. For each m&equil;1,2,... the sequence is demarcated by entrance to the recurrent event. The subsequences between the demarcation points thus form independent epochs by assumption. Classical techniques then yield variance estimates for the number of ones and zeros in the epoch as well as an estimate of the covariance of the ones and zeros. A quadratic equation in [?] is solved to obtain an interval estimate.