A conditionally heteroskedastic time series model for certain South African stock price returns

Abstract

ABSTRACTThe distributional properties of returns data have important implications for financial models and are of particular importance in risk-scenario simulation, volatility prediction and in the event of financial crisis. We present simple time-series models that capture the heteroskedasticity of financial time series and incorporate the effect of using heavy-tailed distributions. These models allow for time-varying volatility, which is an important extension of the conventional methodology. The models are an augmentation of the GARCH class of models, but allow for conditionally normal inverse Gaussian and variance gamma distributed errors. As in previous studies, this new approach permits a distinction between conditional heteroskedasticity and a conditionally leptokurtic distribution, but, compared with the well-known GARCH-t model, it allows us to capture the asymmetric behaviour observed in actual returns series. The practical applicability of the models is confirmed by implementing a fitting procedure to a carefully chosen set of South African stock price returns.