Forecasting volatility of stock indices: Improved GARCH-type models through combined weighted volatility measure and weighted volatility indicators

This paper proposes an unbiased combined weighted (CW) volatility measure and weighted volatility indicators (WVI) that integrates the return- and range-based volatility measures to model the dynamics volatility of stock returns. The main feature of the CW measure is that it is formulated based on the weighted inter- and intra-price information to quantify the volatility directly, while the WVI effectively identifies signals on the shift of volatility. Empirical analysis using five stock indices demonstrates that the CW measure, utilising squared returns in combination with range-based Garman-Klass volatility measure, exhibits the lowest losses based on root mean squared error and quasi-likelihood when compared to 5-minute realised volatility as a proxy for true volatility. Furthermore, we investigate the feasibility of incorporating the CW measure and WVI as the exogenous variable(s) in the generalised autoregressive conditional heteroscedasticity (GARCH)-type models to enhance the forecasting performance. The findings indicate that the GARCH-CW-WVI and EGARCH-CW-WVI models exhibit superior in-sample model fit based on the Akaike information criterion than the existing GARCH and EGARCH models. Moreover, our proposed models also offer the best out-of-sample forecasts evaluated using various loss functions and further tested using Hansen’s model confidence set based on the mean squared error loss. Different risk levels of value-at-risk (VaR) and expected shortfall (ES) forecasts based on GARCH-CW-WVI and EGARCH-CW-WVI models are computed and examined with various backtests to confirm the accuracies of VaR and ES forecasts.