Mathematics, Vol. 12, Pages 3966: Evaluating Predictive Accuracy of Regression Models with First-Order Autoregressive Disturbances: A Comparative Approach Using Artificial Neural Networks and Classical Estimators

Mathematics, Vol. 12, Pages 3966: Evaluating Predictive Accuracy of Regression Models with First-Order Autoregressive Disturbances: A Comparative Approach Using Artificial Neural Networks and Classical Estimators

Mathematics doi: 10.3390/math12243966

Authors: Rauf I. Rauf Masad A. Alrasheedi Rasheedah Sadiq Abdulrahman M. A. Aldawsari

In the last decade, the size and complexity of datasets have expanded significantly, necessitating more sophisticated predictive methods. Despite this growth, limited research has been conducted on the effects of autocorrelation within widely used regression methods. This study addresses this gap by investigating how autocorrelation impacts the predictive accuracy and efficiency of six regression approaches: Artificial Neural Network (ANN), Ordinary Least Squares (OLS), Cochrane–Orcutt (CO), Prais–Winsten (PW), Maximum Likelihood Estimation (MLE), and Restricted Maximum Likelihood Estimation (RMLE). The study evaluates each method’s performance on three datasets characterized by autocorrelation, comparing their predictive accuracy and variability. The analysis is structured into three phases: the first phase examines predictive accuracy across methods using Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE); the second phase evaluates the efficiency of parameter estimation based on standard errors across methods; and the final phase visually assesses the closeness of predicted values to actual values through scatter plots. The results indicate that the ANN consistently provides the most accurate predictions, particularly in large sample sizes with extensive training data. For GDP data, the ANN achieved an MSE of 1.05 × 109, an MAE of 23,344.64, and an MAPE of 81.66%, demonstrating up to a 90% reduction in the MSE compared to OLS. These findings underscore the advantages of the ANN for predictive tasks involving autocorrelated data, highlighting its robustness and suitability for complex, large-scale datasets. This study provides practical guidance for selecting optimal prediction techniques in the presence of autocorrelation, recommending the ANN as the preferred method due to its superior performance.