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Gaussian Approximation for Lag‐Window Estimators and the Construction of Confidence Bands for the Spectral Density

Author

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  • Jens‐Peter Kreiß
  • Anne Leucht
  • Efstathios Paparoditis

Abstract

In this article, 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.

Suggested Citation

  • Jens‐Peter Kreiß & Anne Leucht & Efstathios Paparoditis, 2026. "Gaussian Approximation for Lag‐Window Estimators and the Construction of Confidence Bands for the Spectral Density," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(1), pages 90-105, January.
    • Handle: RePEc:bla:jtsera:v:47:y:2026:i:1:p:90-105
    DOI: 10.1111/jtsa.12826
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