Central limit theorem for Fourier transforms of stationary processes

Central limit theorem for Fourier transforms of stationary processes

Magda Peligrad and Wei Biao Wu

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

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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Primary Subjects: 60F05

Secondary Subjects: 60F17

Keywords: Fourier transform; spectral analysis; martingale; central limit theorem; stationary process

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1282053779
Digital Object Identifier: doi:10.1214/10-AOP530
Zentralblatt MATH identifier: 05793429
Mathematical Reviews number (MathSciNet): MR2722793

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