Edgeworth expansions for a class of spectral density estimators and their applications to interval estimation

Article Type

Research Article

Publication Title

Statistica Sinica

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.

First Page

2591

Last Page

2608

DOI

10.5705/ss.202017.0121

Publication Date

10-1-2018

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