Author(s): Carl H. Korkpoe, Emmanuel K. Oseifuah
The study used the Autoregressive Conditional Density (ACD) methodology to model time-varying higher moments in the distribution of returns of the JSE All Share Index (JSE-ALSI) over the15-year period, January 2003 to December 2017. We found that the fourth higher moment beyond the variance is needed to completely describe the distribution of returns during the sample period. This was done with the GARCH (1, 1)-ACD-NIG model. Further, backtests were performed using the ACD and GARCH models at 1% and 5% to ascertain the soundness of these models in estimating firm risk exposures. The analysis generated the correct number of VaR exceedances which are independent too; hence we fail to reject either model as suitable for the estimation of risk. We also performed the Berkowitz independence test at the 1% quantile. Both models generated higher p-values with the GARCH model seemingly providing a slightly better fit in the tails. Overall, the results show that the fourth moment is needed to completely characterize the distribution of the returns during the sample period but the various goodness-of-fit tests are unable to discriminate clearly between the GARCH(1,1) and the GARCH(1, 1)-ACD-NIG models.