Estimating South Africa’s Growth Risk using GARCH-Type Models and Heavy-Tailed Distributions

The daily returns from financial market variables, such as stock indices, exhibit empirical distributions that are often heavy or semi-heavy or more Gaussian-like tailed. Estimating value-at-risk (VaR) and other risk measures such as conditional VaR (expected shortfall) depend highly on the distributional characteristics of the stock returns. The main objective of this study is to investigate the relative performance of the generalized hyperbolic skew Student-t and Pearson type-IV distributions governing the generalized autoregressive conditional heteroscedasticity (GARCH) innovations in estimation of the VaR for the daily returns from the FTSE/JSE growth index (J280). The results show that the ARMA(1,1)-EGARCH(1,1) model with a generalized hyperbolic skew Student-t distribution governing the innovations outperforms the competing models at estimating the VaR at a 95% level. Results also show that the ARMA(1,1)-EGARCH(1,1) model with a Pearson type-IV distribution governing the innovations outperforms the other competing models at estimating the VaR at all levels for the long position. This study recommends that the ARMA(1,1)-EGARCH(1,1) model with generalized hyperbolic skew Student-t and Pearson type-IV distributions be used in the modeling of daily returns from stock indices