Beyond Normality: OGELAD Error Distribution in Energy Prices Volatility Forecasting

Abstract

 Accurate modelling and forecasting of energy price volatility, particularly crude oil, is essential for effective risk management, derivative pricing, and energy policy formulation. Traditional GARCH models often rely on the assumption of normally distributed errors, which fails to capture the fat tails and asymmetry typically observed in energy markets. This study investigates the impact of error distribution choice on volatility forecasting by evaluating the performance of a newly proposed error distribution—the Odd Generalized Exponential Laplace Distribution (OGELAD)—alongside three established non-normal distributions (Student’s t, GED, and Skewed t) within three asymmetric GARCH frameworks: EGARCH (1,1), TGARCH (1,1), and GJR-GARCH (1,1). Using daily crude oil return data from the West Texas Intermediate (WTI) benchmark spanning January 2010 to December 2022 (a total of 3,285 observations), each model was fitted and assessed using log-likelihood values and information criteria (AIC, BIC, HQIC). All models yielded statistically significant parameters (p < 0.05), and residual diagnostics confirmed the removal of conditional heteroscedasticity. Among all combinations, the GJR-GARCH (1,1) model with OGELAD-distributed innovations achieved the highest log-likelihood value of 4,251.36 and the lowest AIC (−8,472.69), BIC (−8,443.17), and HQIC (−8,461.22). In the 30-day out-of-sample forecast evaluation, this model also demonstrated the lowest Root Mean Square Error (RMSE = 0.0382) and Mean Absolute Error (MAE = 0.0265), confirming its superior predictive performance. These results establish the OGELAD distribution as a more effective alternative for capturing the distributional characteristics of energy price returns, thus enhancing the reliability of volatility forecasts and informing better financial and policy decisions.