Fourier transforms of stationary processes
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- by Wei Biao Wu PDF
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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.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 285-293
- MSC (2000): Primary 60F05, 60F17; Secondary 60G35
- DOI: https://doi.org/10.1090/S0002-9939-04-07528-8
- MathSciNet review: 2086221