Inference of weighted $V$-statistics for nonstationary time series and its applications
The Annals of Statistics · 2014 · Volume 42 · Issue 1
Abstract
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.
Keywords
$V$-Statistics, 60F05, 62E20, Degeneracy, Fourier transform, locally stationary time series, nondegeneracy, nonparametric inference, spectral analysis
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