The Annals of Probability

Central limit theorem for Fourier transforms of stationary processes

Magda Peligrad and Wei Biao Wu

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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.

Article information

Source
Ann. Probab., Volume 38, Number 5 (2010), 2009-2022.

Dates
First available in Project Euclid: 17 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1282053779

Digital Object Identifier
doi:10.1214/10-AOP530

Mathematical Reviews number (MathSciNet)
MR2722793

Zentralblatt MATH identifier
1206.60026

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles

Keywords
Fourier transform spectral analysis martingale central limit theorem stationary process

Citation

Peligrad, Magda; Wu, Wei Biao. Central limit theorem for Fourier transforms of stationary processes. Ann. Probab. 38 (2010), no. 5, 2009--2022. doi:10.1214/10-AOP530. https://projecteuclid.org/euclid.aop/1282053779


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