Japanese stock markets have two types of breaks, overnight and lunch, during which no trading occurs, causing an inevitable increased variance in estimating daily volatility via a naive realized variance (RV). In order to perform a more stabilized estimation, we modify Hansen and Lunde's weighting technique. As an empirical study, we estimate optimal weights by using a particular approach for Japanese stock data listed on the Tokyo Stock Exchange, and then compare the forecast performance of weighted and non-weighted RV through an autoregressive fractionally integrated moving average model. The empirical result indicates that the appropriate use of the optimally weighted RV can lead to remarkably smaller estimation variance compared with the naive RV, in many series. Therefore a more accurate forecasting of daily volatility data is obtained. Finally, we perform a Monte Carlo simulation to support the empirical result.