Gaussian Approximation for Lag-Window Estimators and the Construction of Confidence bands for the Spectral Density

TL;DR

This paper develops a Gaussian approximation approach for constructing confidence bands for spectral density in stationary time series, enabling validation of bootstrap methods and analysis of their convergence rates.

Contribution

It introduces a Gaussian approximation framework for lag-window spectral density estimators, facilitating the validation and rate analysis of bootstrap confidence bands.

Findings

Gaussian approximation enables validation of bootstrap methods.

The paper derives convergence rates for the bootstrap procedure.

Simulation studies illustrate finite sample performance.

Abstract

In this paper we consider the construction of simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for classical lag-window spectral density estimators evaluated at the set of all positive Fourier frequencies. The Gaussian approximation opens up the possibility to verify asymptotic validity of a multiplier bootstrap procedure and, even further, to derive the corresponding rate of convergence. A small simulation study sheds light on the finite sample properties of this bootstrap proposal.