Modelling and forecasting volatility of JSE sectoral indices: a Model Confidence Set exercise

Abstract

Volatility plays an important role in option pricing and risk management. It is crucial that volatility is modelled as accurately as possible in order to forecast with confidence. The challenge is in the selection of the ‘best’ model with so many available models and selection criteria. The Model Confidence Set (MCS) solves this problem by choosing a group of models that are equally good. A set of GARCH models were estimated for several JSE indices and the MCS was used to trim the group of models to a subset of equally superior models. Using the Mean Squared Error to evaluate the relative performance of the MCS, GARCH (1,1) and Random Walk, it was found that the MCS, with an equally weighted combination of models, performed better than the GARCH (1,1) and Random Walk for instances where volatility in the returns data was high. For instances of low volatility in the returns, the GARCH (1,1) had superior 5-day forecasts but the MCS had better performance for 10-days and greater. The EGARCH (2,1) volatility model was selected by the MCS for 5 out of the 6 indices as the most superior model. The Random Walk was shown to have better long term forecasting performance.