Sequential Estimation of the Mean of a First-Order Stationary Autoregressive Process

Abstract

This paper considers the problem of sequential point and fixed-width confidence interval estimation of the location parameter when the errors form an autoregressive process with unknown scale and autoregressive parameters. The sequential point estimator considered here is based on sample mean and is shown to be asymptotically risk efficient as the cost per observation tends to zero. The sequential interval estimator is shown to be asymptotically consistent and the corresponding stopping rule is shown to be asymptotically efficient as the width of the interval tends to zero.