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

摘要

We investigate the behavior of Fourier transforms for a wide class ofnonstationary nonlinear processes. Asymptotic central and noncentral limittheorems are established for a class of nondegenerate and degenerate weighted$V$-statistics through the angle of Fourier analysis. The established theoryfor $V$-statistics provides a unified treatment for many important time andspectral domain problems in the analysis of nonstationary time series, rangingfrom nonparametric estimation to the inference of periodograms and spectraldensities.