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.
Highlights
Consider the general nonlinear regression model defined by yt = g + ut, (1)where xt = is a k-dimensional vector of regressors and β = (β1, . . . , βk) is a k-dimensional vector of unknown parameters
This paper proposes an improved likelihood-based method to test for first-order moving average in the disturbances of nonlinear regression 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
Summary
Nguimkeu and Rekkas [1] proposed a third-order procedure to accurately test for autocorrelation in the disturbances, ut, of the nonlinear regression model (1) when only few data are available. In this paper we show how the same approach can be used to test for first-order moving average, MA(1), disturbances in such models. Chang et al [7] assumed the mean to be some constant μ whereas the current paper considers a general form for the mean function to be g(xt, β), where β is a vector of unknown parameters and the function g(⋅, ⋅) is known. Numerical studies including Monte Carlo simulations as well as real data applications on aggregate consumption and mobile cellular usage in the US are presented in Section 3 to illustrate the superior accuracy of the proposed method over existing ones and its usefulness in practice.
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