Robust Forecasting under Conditional Heteroskedasticity: Evidence from ARMA–GARCH and Smooth Transition GARCH Models
Akintunde Mutairu Oyewale *
Department of Statistics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Aim: This study compares the efficiency of linear and non-linear time-varying volatility models in describing the conditional mean and variance dynamics of macroeconomic variables using monthly Nigerian exchange-rate data from January 2000 to December 2025. Python and EViews were used for the analysis. The study examines whether regime-specific non-linear dynamics produce better forecasting results than traditional linear models.
Study Design: A quantitative, comparative time-series econometric research design was employed.
Place and Duration of Study: Monthly Nigerian exchange-rate data covering January 2000 to December 2025 were collected for the study.
Methodology: The Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) and Smooth Transition Generalized Autoregressive Conditional Heteroskedasticity (ST-GARCH) models were used. The modelling process involved unit-root testing, model specification, maximum-likelihood estimation, model diagnostics, and out-of-sample forecast-performance evaluation. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Theil’s U were used to evaluate accuracy.
Results: The series was found to be integrated of order one, I(1), according to the Augmented Dickey-Fuller (ADF) test, necessitating first differencing to achieve stationarity. The sample autocorrelation and partial autocorrelation functions (ACF and PACF) confirmed strong serial dependence and finite autoregressive properties. The results also indicated high persistence and non-linear effects in the Nigerian exchange rate. Both models demonstrated reasonable predictive power. Nevertheless, the ST-GARCH model outperformed the ARMA-GARCH model because it produced lower RMSE, MAE, MAPE, and AIC values, indicating better predictive performance, particularly during volatile periods.
Conclusion: The empirical results indicate that, although the symmetric ARMA-GARCH model provides a valid framework during relatively tranquil periods, non-linear specifications better account for intervals of structural instability. Overall, the LST-GARCH model demonstrated the greatest statistical adequacy, with a log-likelihood of -956.23, an AIC of 1932.46, and the lowest estimated residual variance of 117.94. Consequently, modelling smooth parameter transitions over time helps to account for structural changes within persistent volatility.
Keywords: Exchange-rate forecasting, conditional heteroskedasticity, ARMA–GARCH, ST-GARCH, ET-GARCH, EST-GARCH, LST-GARCH, volatility persistence, regime transition, forecast accuracy