We propose novel realized dynamic conditional correlation (Realized DCC) models with measurement errors to forecast the covariance of asset returns. This study aims to forecast the conditional covariance matrix of asset returns and to ensure the bound, \(\rho \in [-1,1]\) , of the forecasted correlation matrix by incorporating the measurement error in estimating the conditional correlation and using the BEKK and HAR models to estimate the conditional correlation matrix using the Fisher z transformation. The proposed models in this study can include measurement error into not only variance estimations but also correlation estimations. These models can keep the persistence of volatility and correlation at high levels when the asymptotic variances of realized volatility and realized correlation are small. By incorporating measurement errors, models can decrease the persistence when the asymptotic variances are large. Our empirical results show that our models which incorporate the measurement error into the correlation estimation make more accurate forecasts than other models which do not incorporate it into the correlation estimation.
