Optimal volatility modeling for Nigeria's external reserves: a comprehensive evaluation of GARCH specifications under non-normal distributions

The volatility of external reserves poses critical challenges for commodity-dependent economies like Nigeria, where fluctuating oil revenues and capital flow instability exacerbate macroeconomic vulnerabilities. This study evaluates optimal volatility modeling for Nigeria’s external reserves by conducting a comprehensive comparison of generalized autoregressive conditional Heteroscedasticity (GARCH) family specifications under non-normal distributions. Using monthly external reserves data from 1981–2023, we assess symmetric (GARCH, GARCH-M) and asymmetric Exponential GARCH (EGARCH), Threshold-GARCH (TGARCH), Power-GARCH (PGARCH)] models with two error distributions [Student’s t and generalized error distribution (GED). Results reveal three key findings: The standard GARCH(1,1) with GED demonstrates superior fit (lowest AIC: -1.8432) and robust forecasting performance (RMSE: 0.336), outperforming asymmetric variants; Volatility exhibits extreme persistence (α+β > 1) but no significant leverage effects, contrasting with financial market studies; and lastly, GARCH-M models failed (RMSE > 1E+20), rejecting risk premium relevance. Diagnostic tests confirm the adequacy of GARCH-GED specifications in eliminating residual heteroskedasticity. The findings suggest that Nigeria’s reserves volatility driven by oil price shocks and structural breaks requires fat-tailed distributions but not asymmetry adjustments. For policymakers, this implies that simpler symmetric models may suffice for reserves risk forecasting, though persistence mandates long-term shock mitigation strategies. The study provides the first systematic evidence on distributional and functional form choices for modeling reserves volatility in commodity-dependent economies.