Confidence intervals using orthonormally weighted standardized time series

Abstract

We extend the standardized time series area method for constructing confidence intervals for the mean of a stationary stochastic process. The proposed intervals are based on orthonormally weighted standardized time series area variance estimators. The underlying area estimators possess two important properties: they are first-order unbiased, and they are asymptotically independent of each other. These properties are largely the result of a careful choice of weighting functions, which we explicitly describe. The asymptotic independence of the area estimators yields more degrees of freedom than various predecessors; this, in turn, produces smaller mean and variance of the length of the resulting confidence intervals. We illustrate the efficacy of the new procedure via exact and Monte Carlo examples. We also provide suggestions for efficient implementation of the method.