Invariance Principle and Berry–Esseen Bound for Error Variance Estimator for Pth-Order Nonlinear Autoregressive Models

Abstract

The invariance principle and Berry–Esseen bound for an error variance estimator based on the residuals are established by using a Taylor expansion and the classical invariance principle and Berry–Esseen bound for independent random variables. Some examples are given to illustrate their applications.

Keywords

• nonlinear autoregressive models
• invariance principle
• Berry–Esseen bound
• error variance estimator
• residuals