INFERENCE OF WEIGHTED V-STATISTICS FOR NONSTATIONARY TIME SERIES AND ITS APPLICATIONS

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.