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arXiv · 1401.4007

Inference of weighted $V$-statistics for nonstationary time series and its applications

Zhou Zhou
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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.

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Zhou Zhou. 2014-01-16. Inference of weighted $V$-statistics for nonstationary time series and its applications. https://doi.org/10.1214/13-aos1184

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