Limit theorems for a class of martingale arrays with applications in nonlinear cointegrating regression

Qiying Wang

Abstract

This paper develops a new asymptotic theory for a broad class of martingales, establishing convergence to limiting distributions that involve a functional of stochastic integrals. The proposed limit theorem substantially extends existing martingale asymptotic theory by accommodating a wider class of dependence structures. As a primary application, the theory is applied to nonlinear regression models with nonstationary time series, yielding a rigorous framework for asymptotic inference on nonlinear least square estimators.

Keywords: Martingale limit theorem; Stochastic integrals; A mixture of normal distributions; Nonlinear cointegrating regression.