On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

TL;DR

This paper investigates the properties of the Whittle estimator for the spectral density parameter of linear noise in continuous-time nonlinear regression models driven by Lévy processes, establishing conditions for its consistency and asymptotic normality.

Contribution

It provides new theoretical results on the consistency and asymptotic normality of the Whittle estimator in Lévy-driven continuous-time nonlinear models.

Findings

Conditions for estimator consistency established

Asymptotic normality proven under certain conditions

Theoretical framework for spectral density parameter estimation

Abstract

A continuous-time nonlinear regression model with L\'evy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are obtained in the paper.