On the Efficacy of ARFIMA, ARTFIMA, and MARFIMA Models in Forecasting Nigerian Crude Oil Prices

Abstract

This study presents a comprehensive evaluation of three advanced long-memory time series models— the Autoregressive Fractionally Integrated Moving Average (ARFIMA), the Autoregressive Tempered Fractionally Integrated Moving Average (ARTFIMA), and the Modified ARFIMA (MARFIMA) — for forecasting Nigerian crude oil prices. The research addresses critical limitations in existing long-memory models, particularly the slow convergence and data truncation issues of traditional ARFIMA models when handling large, nonstationary datasets with long-range dependence. We propose MARFIMA as an enhanced alternative that incorporates a sequential differencing filter, extending the fractional differencing parameter to the range 1 < d < 1.5 for improved trend removal and memory retention. Using Nigerian daily crude oil prices data from July 2012 to February 2024, we compared the model's performance using rigorous statistical tests, including the Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (SBIC), Root Mean Square Error (RMSE), and Normalized Mean Square Error (NMSE). The results demonstrate that the MARFIMA model has superior performance, with significantly lower forecast errors (32.5% reduction in RMSE compared to ARFIMA and 42.7% reduction in RMSE compared to ARTFIMA) and better model fit. The findings have important implications for energy economists, policymakers, and financial analysts dealing with volatile commodity markets, offering a more robust framework for oil price forecasting in developing economies.