Statistica Sinica 28 (2018), 2591-2608
Abstract: In this paper we obtain valid Edgeworth expansions (EEs) for a class of spectral density estimators of a stationary time series. The spectral estimators are based on tapered periodograms of overlapping blocks of observations. We give conditions for the validity of a general order EE under an approximate strong mixing condition on the random variables. We use the EE results to study higher order coverage accuracy of confidence intervals (CIs) based on Studentization and on Variance Stabilizing transformation. It is shown that the accuracy of the CIs critically depends on the length of the blocks employed. We use the EE results to determine the optimal orders of the block lengths for one- and two-sided CIs under both methods. Theoretical results are illustrated with a moderately large simulation study. We dedicate this paper to the memory of Professor Peter Hall who made fundamental contributions to asymptotic theory of Statistics and extensively used EEs to study higher order coverage properties of CIs.
Key words and phrases: Confidence intervals, frequency domain, stationary, studentization, taper, variance stabilizing transformation.