Modelling of Regression with Non-Gaussian AR Errors

Abstract

This paper presents a new forecasting methodology aimed at addressing challenges in regression models where the residuals exhibit both autocorrelated errors and non-Gaussian innovations. Traditional regression models often assume independent and normally distributed errors; however, in many real-world applications, these assumptions are violated, leading to biased and inefficient parameter estimates. We employ the Optimal Estimating Function (EF) method and the Cochran-Orcutt procedure to effectively handle autocorrelation and non-Gaussian innovations in the error structure. Through comprehensive simulation studies, we evaluate the robustness and efficiency of this combined approach in estimating the model parameters under various scenarios. The methodology is further validated by applying it to both simulated and real-world datasets, showcasing its versatility and practical relevance. For the real data analysis, we use the Rubber dataset, which consists of observations on rubber production and the area of cultivation over a specified period. This application demonstrates the practical utility of the proposed method in dealing with non-Gaussian autocorrelated errors, providing more accurate forecasts and parameter estimates than traditional methods.