Exploring the dynamics of the ZAR/USD Exchange Rate volatility using the FGARCH and FIRST-ORDER BETA-SKEW-T-EGARCH Models

Abstract

The effect of exchange rate fluctuations on international trade, investment choices, and economic stability has captured the attention of economists, policymakers, and market participants for a long time. This study investigates the dynamics of the ZAR/USD exchange rate volatility using advanced econometric models: the Family GARCH (fGARCH) model and the First- Order Beta-Skew-T-Generalised Autoregressive Conditional Heteroskedasticity (First-Order Beta-Skew-T-EGARCH) model. The ZAR/USD exchange rate is an important indicator for global trade, investment, and economic stability. However, traditional volatility models often struggle to fully capture its complex behaviour. This research aims to fill this gap by using the fGARCH and the First-Order Beta-Skew-T-EGARCH models to better understand volatility characteristics, including long-memory effects, asymmetry, and skewness, using the daily data from 5/01/2000 to 01/10/2024. The sGARCH and fGARCH were first compared using the following five error distributions: Student’s t, skewed Student’s t, generalised error, skewed generalised error distributions, and generalised hyperbolic distribution. The model selection is based on the information criteria with the lowest AIC, BIC, Shibata, and Hannan-Quinn. The fGARCH(1,1) model has the lowest AIC compared to the sGARCH model. The covariate effects were analysed for day, month, trend, oil, and platinum. The trend is statistically significant (p = 0.007) and positively influences the ZAR/USD market. Beta-Skew- T-EGARCH with one and two components displayed a significant spike in both 2008 and 2009 due to a global financial crisis. The two-component model provides a better fit with the lowest BIC (3.242162) and a high Log- Likelihood of -748.464826. Volatility was analysed over seven days using one and two-component models. The one-component level remained high, indicating persistent volatility, while the two-component model showed low conditional volatility. This suggests that the two-component model outperforms the one-component model, effectively reducing uncertainty. The outcomes of this research will contribute to the refinement of models for understanding and predicting volatility in the foreign exchange markets, providing valuable implications for financial decision-makers and policy-makers.