Resampling the autocovariance estimator in stationary gaussian processes

Abstract

A resampling algorithm is proposed for the estimator of the autocovariance function of stationary Gaussian processes. The frequency domain representation of the estimator is used and the resampling is conducted in the frequency domain. The method is shown to give bootstrap replicates of the estimator which asymptotically have a distribution which is close to the true sampling distribution of the estimator. The proposed method is also shown to work for certain functions of the estimator such as the autocorrelation estimator. Some simulation results are also given to illustrate the performance of the estimator.