Abstract: We introduce a new univariate score-driven model which explicitly incorporates long memory dynamics in the conditional variance of daily returns. First, we model the conditional variance as a fractionally integrated (FI) process, and importantly, allow the long memory parameter to cross the stationarity boundary d=0.5. Second, we adopt a heterogeneous autoregressive (HAR) model that parsimoniously approximates long memory dynamics through mixed-frequency mean components. The new model accommodates heavy-tailed densities for both the daily returns and realised measures. This choice of observational densities ensures an automatic correction for the influential observations through the score. In an empirical study conducted for fifteen individual components of the DJI index over the period 2001-2010, we find that likelihood favours the new FI model with d>0.5. Our out-of-sample analysis identifies that accounting for long memory through either the FI or the HAR form is particularly useful for volatility level evaluation and return risk assessment during non-crisis periods.