Fourier transforms of stationary processes

Wu, Wei

doi:10.1090/S0002-9939-04-07528-8

Fourier transforms of stationary processes
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by Wei Biao Wu PDF

Proc. Amer. Math. Soc. 133 (2005), 285-293 Request permission

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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