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

Abstract

This study investigates and explores the volatility dynamics of the South African rand against the US dollar (ZAR/USD) using the Family GARCH (fGARCH) model and the First-Order Beta-Skew-T-Generalised Autoregressive Conditional Heteroskedasticity (Beta-Skew-T-EGARCH) model. Currency volatility across the globe, uncertainties, and instability in emerging markets have become increasingly consequential for trade flows, investment allocation, and macroeconomic management. The ZAR/USD serves as a benchmark of South Africa’s economic wealth and vulnerability to external shocks and is one of the most valued, significant, and heavily traded pairings of emerging market currencies. Simple standard GARCH (sGARCH) is one of the most useful models for exchange rate volatility; however, the sGARCH model has some limitations: it fails to accommodate or allow the long memory effects, skewness distribution, and leverage dynamics consistently observed in emerging-market currency returns. This study addresses these limitations by using the fGARCH model, which includes the most popular GARCH models and Beta-Skew-T-EGARCH for daily ZAR/USD returns ranging from 5 January 2000 to 1 October 2024. Five innovation distributions are used for evaluation and comparison under fGARCH and sGARCH, namely generalised hyperbolic (GH), generalised error (GED), skewed Student’s t (SSTD), skewed generalised error (SGED), and Student’s t (STD), with model fitness criteria assessed using the Shibata criterion (SIC), Hannan–Quinn criterion (HQ), Bayesian information criterion (BIC), and Akaike information criterion (AIC), choosing the specification with the lowest overall penalty. It is found that the fGARCH(1,1) model fitted to return-frequency data under the SSTD achieves the lowest AIC, outperforming sGARCH. The study also includes an analysis among covariates, which are day, month, trend, oil, and platinum; the trend variable is a statistically significant predictor, with p = 0.007, showing a positive influence on ZAR/USD volatility. The Beta-Skew-T-EGARCH model with two components divides volatility into long-run and short-run components, which is found to deliver a superior fit over the one-component variant, evidenced by a lower BIC (3.068435) and a higher log-likelihood (−748.464826). The two components confirm that the model captures declining conditional volatility, whereas the one-component model sustains persistence in the evaluated estimates.