Evaluation of Error Distributions in Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MGARCH) Models: Dynamic Conditional Correlation.

Abstract:

This study investigates the impact of alternative error distributions on the performance of the Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MGARCH)–Dynamic Conditional Correlation (DCC) model in analysing volatility dynamics among Nigerian financial assets. Using daily data on Nigerian stock prices, Brent crude oil prices, and the All-Share Index from March 2017 to May 2025, the MGARCH-DCC(1,1) models were estimated under four distributions Normal, Student-t, Skewed Student-t, and Generalized Error Distribution (GED). The results indicate significant volatility persistence across all assets, with beta coefficients ranging from 0.678 to 0.875, confirming long memory in conditional variances. The ARCH coefficients (α₁) ranged between 0.113 and 0.322, signifying substantial short-term volatility reactions to shocks. The DCC parameters (a₁ = 0.013–0.018 and b₁ = 0.658–0.702) reveal that correlations evolve gradually, reflecting a strong persistence in co-movement among the markets. Furthermore, the shape parameters for the t and GED distributions (e.g., ν = 3.17–6.01) confirm heavy tails, while the skewness parameters close to 1.00 indicate mild asymmetry. Overall, the Skewed Student-t and Student-t error distributions outperform the Gaussian model, effectively capturing volatility clustering and fat-tailed behaviour in Nigerian financial data. These findings highlight the importance of selecting appropriate error structures for accurate volatility modelling, forecasting, and risk assessment in emerging markets.