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arXiv · 2407.12316

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

Jens-Peter Kreiss·Anne Leucht·Efstathios Paparoditis
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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.

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Jens-Peter Kreiss, Anne Leucht, Efstathios Paparoditis. 2024-07-17. Gaussian Approximation for Lag-Window Estimators and the Construction of Confidence bands for the Spectral Density. https://arxiv.org/abs/2407.12316

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