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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fourier transforms of stationary processes


Author: Wei Biao Wu
Journal: Proc. Amer. Math. Soc. 133 (2005), 285-293
MSC (2000): Primary 60F05, 60F17; Secondary 60G35
Published electronically: May 20, 2004
MathSciNet review: 2086221
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are established for almost all frequencies as well as for a given frequency. Applications to the widely used linear processes and iterated random functions are discussed. Our results shed new light on the foundation of spectral analysis in that the asymptotic distribution of the periodogram, the fundamental quantity in the frequency-domain analysis, is obtained.


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Additional Information

Wei Biao Wu
Affiliation: Department of Statistics, The University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Email: wbwu@galton.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07528-8
PII: S 0002-9939(04)07528-8
Keywords: Spectral analysis, linear process, martingale central limit theorem, periodogram, Fourier transformation, nonlinear time series
Received by editor(s): March 24, 2003
Received by editor(s) in revised form: June 27, 2003, and September 18, 2003
Published electronically: May 20, 2004
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2004 American Mathematical Society