The Role of Innovation Distributions in Forecasting Brent Crude Oil Volatility Using Univariate GARCH Models

Abstract

This study investigates the impact of different error distributions on the performance of univariate GARCH-family models in modeling and forecasting the volatility of Brent crude oil returns from January 2014 to May 2025. Descriptive analysis reveals pronounced fluctuations, volatility clustering, and asymmetric behavior in the return series, including major price declines around 2015–2016 and early 2020, followed by a surge in 2021–2022. Stationarity of returns is confirmed using Augmented Dickey-Fuller and Phillips-Perron tests (ADF = −53.52, p = 0.0001), while ARCH-LM tests indicate significant conditional heteroskedasticity (Chi² = 365.97, p < 0.01), justifying the use of GARCH-type models. Parameter estimates from sGARCH, EGARCH, and TGARCH models highlight strong volatility persistence (β₁ ≈ 0.92 0.98) and significant leverage effects (γ₁ ≈ 0.16–0.44). Model comparison across Normal, GED, Student’s t, and Skewed Student’s t distributions shows that heavy-tailed and skewed distributions improve fit, with the TGARCH (1,1) model under the Skewed Student’s t distribution providing the best performance (LogLik = 9836.94, AIC = −6.7076). The findings underscore the importance of selecting appropriate error distributions to accurately capture volatility dynamics, leverage effects, and extreme market movements, providing guidance for risk management and forecasting in oil markets.