CONSISTENCY OF SEVERAL VARIANTS OF THE STANDARDIZED TIME-SERIES AREA VARIANCE ESTIMATOR

In statistical analysis of stationary time series or in steady-state s imulation output analysis, it is desired to find consistent estimates of the process variance parameter. Here, we consider variants of the a rea estimator of standardized time series, namely, the weighted area a nd the Cramer-von Mises area estimators, and provide their consistency , in the strong sense and. mean-square sense. A sharp bound for the (a symptotic) variance of these estimators is obtained. We also present a central limit theorem for the weighted area estimator: this gives a r ate of convergence of this estimator, as well as a confidence interval for the variance parameter. (C) 1995 John Wiley & Sons, Inc.