We obtain intraday data on three stock indices listed on the Taiwan Stock Exchange (TWSE), and then analyse the data by incorporating an overnight returns indicator into the 'Heterogeneous Auto-Regressive' (HAR) model of realized volatility. Our overall aim is to enhance the forecasting of future volatility. Our findings demonstrate that the modified model significantly improves the forecasting performance of future realized volatility, with our results also being found to continue to hold for both in sample and out of sample forecasts.