Confidence Interval Estimation for the Variance Parameter of Stationary Processes

Asymptotic confidence interval estimators of the variance parameter \sigma ² = lim_{n -> \infty} n Var((1/n) \sum ⁿ_{i = 1} X_i) are described in this paper for observations X₁, X₂,...,X_n from a strictly stationary phi-mixing stochastic process. They are based on asymptotic properties of the standardized time series of observations from the process. The new point and interval estimators for the variance parameter are compared to the classical batch means estimator. The results show that the new estimators have asymptotic properties that clearly dominate the classical estimator. Also, asymptotic confidence interval estimators for the ratio of two variance parameters representing two independent processes are discussed.