Long memory, realized volatility and HAR models

The presence of long memory in Realized Volatility (RV) is a widespread stylized fact. The origins of long memory in RV have been attributed to jumps, structural breaks, non-linearities, or pure long memory. An important development has been the Heterogeneous Autoregressive (HAR) model and its extensions. This paper assesses the separate roles of fractionally integrated long memory models, extended HAR models and time varying parameter HAR models. We find that the presence of the long memory parameter is often important in addition to the HAR models.