Translator Disclaimer
April 2003 A necessary and sufficient condition for asymptotic independence of discrete Fourier transforms under short- and long-range dependence
S. N. Lahiri
Ann. Statist. 31(2): 613-641 (April 2003). DOI: 10.1214/aos/1051027883

Abstract

Let $\{X_t\}$ be a stationary time series and let $d_T(\lambda)$ denote the discrete Fourier transform (DFT) of $\{X_0,\ldots,X_{T-1}\}$ with a data taper. The main results of this paper provide a characterization of asymptotic independence of the DFTs in terms of the distance between their arguments under both short- and long-range dependence of the process $\{X_t\}$. Further, asymptotic joint distributions of the DFTs $d_T(\lambda_{1T})$ and $d_T(\lambda_{2T})$ are also established for the cases $T(\lambda_{1T}- \lambda_{2T})=O(1)$ as $T\to\infty$ (asymptotically close ordinates) and $|T(\lambda_{1_T}-\lambda_{2_T})|\to\infty$ as $T\to\infty$ (asymptotically distant ordinates). Some implications of the main results on the estimation of the index of dependence are also discussed.

Citation

Download Citation

S. N. Lahiri. "A necessary and sufficient condition for asymptotic independence of discrete Fourier transforms under short- and long-range dependence." Ann. Statist. 31 (2) 613 - 641, April 2003. https://doi.org/10.1214/aos/1051027883

Information

Published: April 2003
First available in Project Euclid: 22 April 2003

zbMATH: 1039.62087
MathSciNet: MR1983544
Digital Object Identifier: 10.1214/aos/1051027883

Subjects:
Primary: 62M10
Secondary: 62E20, 62M15

Rights: Copyright © 2003 Institute of Mathematical Statistics

JOURNAL ARTICLE
29 PAGES


SHARE
Vol.31 • No. 2 • April 2003
Back to Top