Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model

Appropriate modelling of the process of volatility has implications for portfolio selection, the pricing of derivative securities and risk management. Further, a large body of research has suggested that both long memory and structural changes simultaneously characterize the structure of financial returns volatility. Given this, in this article, we aim to model conditional volatility of the returns of the Dow Jones Islamic Market World Index (DJIM), interest on which has come to the fore following the need for renovation of the conventional financial system, in the wake of the recent global financial crisis. To model the conditional volatility of the DJIM returns, accounting for both long memory and structural changes, we allow the parameters in the conditional variance equation of the fractionally integrated generalized autoregressive conditional heteroscedasticity (FIGARCH) model to be time dependent, such that the parameters evolve smoothly over time based on a logistic smooth transition function, yielding a fractionally integrated time-varying generalized autoregressive conditional heteroscedasticity (FITVGARCH) model. Our results show that, in terms of model diagnostics and information criteria, as well as, portfolio allocation, the FITVGARCH model performs better than the FIGARCH model in explaining conditional volatility of the DJIM returns, thus, highlighting the need to model simultaneously long memory and structural changes in the volatility process of asset returns.