This paper explores the use of realized volatility, a measure derived from intraday data, in estimating stochastic volatility (SV) models. The authors derive the moments and asymptotic distribution of the realized volatility error, which is the difference between realized volatility and the discretized integrated volatility. They show that this error is approximately mixed Gaussian and can be substantial, highlighting the need for more accurate estimates of actual volatility. The paper discusses the properties of realized volatility, including its autocorrelation function and variance, and provides a method to estimate actual volatility using a linear state space representation and the Kalman filter. The authors also demonstrate the effectiveness of model-based estimators over model-free methods, particularly in reducing mean-square error. They apply these methods to real data, showing that realized volatility can be accurately estimated using intraday data, and that the fit of SV models improves with more flexible volatility processes. The paper concludes with a discussion of extensions, including the estimation of parameters in SV models and the handling of diurnal effects and leverage effects.This paper explores the use of realized volatility, a measure derived from intraday data, in estimating stochastic volatility (SV) models. The authors derive the moments and asymptotic distribution of the realized volatility error, which is the difference between realized volatility and the discretized integrated volatility. They show that this error is approximately mixed Gaussian and can be substantial, highlighting the need for more accurate estimates of actual volatility. The paper discusses the properties of realized volatility, including its autocorrelation function and variance, and provides a method to estimate actual volatility using a linear state space representation and the Kalman filter. The authors also demonstrate the effectiveness of model-based estimators over model-free methods, particularly in reducing mean-square error. They apply these methods to real data, showing that realized volatility can be accurately estimated using intraday data, and that the fit of SV models improves with more flexible volatility processes. The paper concludes with a discussion of extensions, including the estimation of parameters in SV models and the handling of diurnal effects and leverage effects.