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September 2010 Central limit theorem for Fourier transforms of stationary processes
Magda Peligrad, Wei Biao Wu
Ann. Probab. 38(5): 2009-2022 (September 2010). DOI: 10.1214/10-AOP530

Abstract

We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all regular sequences. Our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram, and it provides a nice blend of harmonic analysis, theory of stationary processes and theory of martingales.

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Magda Peligrad. Wei Biao Wu. "Central limit theorem for Fourier transforms of stationary processes." Ann. Probab. 38 (5) 2009 - 2022, September 2010. https://doi.org/10.1214/10-AOP530

Information

Published: September 2010
First available in Project Euclid: 17 August 2010

zbMATH: 1206.60026
MathSciNet: MR2722793
Digital Object Identifier: 10.1214/10-AOP530

Subjects:
Primary: 60F05
Secondary: 60F17

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 5 • September 2010
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