Exploring the Dynamics of the ZAR/USD Exchange Rate Volatility Using the fGARCH and First-Order Beta-Skew-T-EGARCH Models

Currency instability in emerging markets has become increasingly consequential for trade flows, investment allocation, and macroeconomic management. This study examines the volatility dynamics of the South African rand against the US dollar (ZAR/USD) using two advanced econometric frameworks: the Family GARCH (fGARCH) model and the first-order Beta-Skew-T-Generalised Autoregressive Conditional Heteroskedasticity (Beta-Skew-T-EGARCH) model. As one of the most heavily traded emerging-market currency pairs, the ZAR/USD serves as a barometer of South Africa’s economic health and vulnerability to external shocks. Standard GARCH specifications, however, impose symmetry constraints that fail to accommodate the long-memory effects, distributional skewness, and leverage dynamics consistently observed in emerging-market currency returns. This study addresses these limitations by deploying the fGARCH and Beta-Skew-T-EGARCH frameworks on daily ZAR/USD returns spanning 5 January 2000 to 1 October 2024. The sGARCH and fGARCH specifications were assessed across five innovation distributions, Student’s t, skewed Student’s t (SSTD), generalised error (GED), skewed generalised error (SGED), and generalised hyperbolic (GH), with model fitness evaluated using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Hannan-Quinn criterion (HQ), and Shibata criterion (SIC), selecting the specification with the lowest combined penalty. The fGARCH(1,1) model fitted to return-frequency data under the SSTD achieves the lowest AIC, outperforming the sGARCH benchmark. Among the covariates examined (day, month, trend, oil, platinum), the trend variable is the sole statistically significant predictor (p = 0.007), exerting a positive influence on ZAR/USD volatility. The two-component Beta-Skew-T-EGARCH model, by decomposing volatility into long-run structural and short-run transient components, delivers a superior fit over the one-component variant, evidenced by a lower BIC (3.068435) and a higher log-likelihood (-748.464826). Seven-day-ahead forecasts confirm that the two-component model captures declining conditional volatility, whereas the one-component model sustains persistently elevated estimates.