Confidence Interval Estimation Using Standardized Time Series

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Abstract
Observations of a stationary stochastic process can be transformed into a standardized time series. This paper presents a lemma giving the asymptotic properties of this standardized series under quite general conditions. In particular, the conditions are satisfied by stationary discrete-event simulations. Confidence intervals can be constructed using this lemma. For illustration, we develop two easily computed interval estimators for the process mean. When independent replications of the series are available, such as in computer simulation experiments, these interval estimators may be combined with the classical confidence interval estimator. These interval estimators also tend to compensate for simulation initialization bias if the sign of the bias is known. In an empirical study using three elementary simulated processes, the interval estimators presented here compare favorably with the classical interval estimator. In a recent paper, Goldsman and Schruben (Goldsman, D., L. Schruben. 1982. Asymptotic properties of some confidence interval estimators. Tech. Rep. 544, School of O.R.I.E., Cornell University, Ithaca, NY.) show that the asymptotic properties of the confidence intervals presented in this paper strictly dominate those of classical confidence intervals.

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