Using Standardized Time Series to Estimate Confidence Intervals for the Difference Between Two Stationary Stochastic Processes

Abstract

This paper discusses confidence interval estimation for the difference between the means of two independent, strictly stationary phi-mixing stochastic processes. The confidence intervals are based on “batched” subseries of the two time series and are obtained by using Schruben's standardized time series method. We compare these intervals with the classical result applied to the batch means, and consider different assumptions on the variances and the number of observations. The comparison results show that the four new estimators for each case have asymptotic properties that clearly dominate the classical estimator. Two applications of these intervals are (1) validating stationary discrete event simulation models, and (2) comparing two alternative policies or system designs via simulation.