Analysing the exponential GARCH model across different sample sizes

The Exponential GARCH model makes provision for the leverage effect and can be used to model the changing variance of a financial time series. In this paper, the changes in volatility, parameter estimates, and forecasting error for different window lengths are investigated. This may indicate an appropriate sample size to use for the Exponential GARCH model. A rolling window methodology was applied across 20 different window lengths on the 1-day log-returns of the FTSE/JSE-ALSI between 27 December 1995 and 15 December 2021, assuming as underlying distribution the Student’s t-distribution. The results are compared to a similar study of Purchase et al. that was done for the Symmetric GARCH model. Results include the sensitivity of the Exponential GARCH parameters, especially for smaller window lengths. The Exponential GARCH model shows stronger forecasting accuracy for window lengths above 500 compared to the Symmetric GARCH model and an overall better fit to the data for all window lengths. The results obtained for the Exponential GARCH model suggest a window length between 600 and 900 to ensure a stable fitted model that can account for market shocks. This aligns with results from the Symmetric GARCH model.