Central limit theorem for fourier transforms of stationary processes.

By Magda Peligrad, Wei Biao Wu. 2009

71 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9659000e2dcee4925c89e7a23082ef96fe9ee62c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Wei Biao Wu
2. Xiaofeng Shao
3. Zhou Zhou
4. Weidong Liu
5. István Berkes
6. Andreas Hagemann
7. Siegfried Hormann
8. Xiaohui Chen

In Mathematical Physics

1. Wei Biao Wu
2. Xiaofeng Shao
3. Richard A. Davis
4. Magda Peligrad
5. Heng Liu

Citations in the corpus

• Asymptotic theory for stationary processes (2011, background): “Theorem 1 in Peligrad and Wu (2010) asserts that, for a regular process, its spectral density function exists almost surely over φ ∈ [0, 2π] with respect to the Lebesgue measure.”