Artificial neural network small‐sample‐bias‐corrections of the AR(1) parameter close to unit root

Abstract

This paper introduces an artificial neural network (ANN) approach to estimate the autoregressive process AR(1) when the autocorrelation parameter is near one. Traditional ordinary least squares (OLS) estimators suffer from biases in small samples, necessitating various correction methods proposed in the literature. The ANN, trained on simulated data, outperforms these methods due to its nonlinear structure. Unlike competitors requiring simulations for bias corrections based on specific sample sizes, the ANN directly incorporates sample size as input, eliminating the need for repeated simulations. Stability tests involve exploring different ANN architectures and activation functions and robustness to varying distributions of the process innovations. Empirical applications on financial and industrial data highlight significant differences among methods, with ANN estimates suggesting lower persistence than other approaches.