Simultaneous confidence bands in spectral density estimation

Michael H. Neumann and Efstathios Paparoditis

Biometrika, 2008, vol. 95, issue 2, 381-397

Abstract: We propose a method for the construction of simultaneous confidence bands for a smoothed version of the spectral density of a Gaussian process based on nonparametric kernel estimators obtained by smoothing the periodogram. A studentized statistic is used to determine the width of the band at each frequency and a frequency-domain bootstrap approach is employed to estimate the distribution of the supremum of this statistic over all frequencies. We prove by means of strong approximations that the bootstrap estimates consistently the distribution of the supremum deviation of interest and, consequently, that the proposed confidence bands achieve asymptotically the desired simultaneous coverage probability. The behaviour of our method in finite-sample situations is investigated by simulations and a real-life data example demonstrates its applicability in time series analysis. Copyright 2008, Oxford University Press.

Date: 2008
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asn005 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:95:y:2008:i:2:p:381-397

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().