Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra

TL;DR

This paper derives the limit Gaussian distribution for weighted nonlinear functionals of Gaussian stationary processes with singular spectra, under broad conditions, aiding in nonlinear regression and inference.

Contribution

It provides the first comprehensive derivation of limit theorems for nonlinear transformations of Gaussian processes with multiple singular spectra.

Findings

Limit Gaussian distribution established for multivariate weighted nonlinear functionals.

Applicable to processes with multiple singular spectra under general conditions.

Enhances tools for nonlinear regression and asymptotic inference.

Abstract

The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.