Open Access
February 2014 Inference of weighted $V$-statistics for nonstationary time series and its applications
Zhou Zhou
Ann. Statist. 42(1): 87-114 (February 2014). DOI: 10.1214/13-AOS1184


We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics through the angle of Fourier analysis. The established theory for $V$-statistics provides a unified treatment for many important time and spectral domain problems in the analysis of nonstationary time series, ranging from nonparametric estimation to the inference of periodograms and spectral densities.


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Zhou Zhou. "Inference of weighted $V$-statistics for nonstationary time series and its applications." Ann. Statist. 42 (1) 87 - 114, February 2014.


Published: February 2014
First available in Project Euclid: 15 January 2014

zbMATH: 1306.62205
MathSciNet: MR3161462
Digital Object Identifier: 10.1214/13-AOS1184

Primary: 60F05 , 62E20

Keywords: $V$-Statistics , Degeneracy , Fourier transform , locally stationary time series , nondegeneracy , nonparametric inference , spectral analysis

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 1 • February 2014
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