Improved Inference for Moving Average Disturbances in Nonlinear Regression Models

Abstract

This paper proposes an improved likelihood-based method to test for first-order moving average in the disturbances of nonlinear regression models. The proposed method has a third-order distributional accuracy which makes it particularly attractive for inference in small sample sizes models. Compared to the commonly used first-order methods such as likelihood ratio and Wald tests which rely on large samples and asymptotic properties of the maximum likelihood estimation, the proposed method has remarkable accuracy. Monte Carlo simulations are provided to show how the proposed method outperforms the existing ones. Two empirical examples including a power regression model of aggregate consumption and a Gompertz growth model of mobile cellular usage in the US are presented to illustrate the implementation and usefulness of the proposed method in practice.