In this thesis, we introduce an extended version of the Realised GAS model by explicitly modelling the long memory dynamics of the conditional variance process. To reflect the long memory property of the process, we use two distinct approaches. The first approach defines the dynamic equation for conditional variance as a fractionally integrated process. The second approach adopts a heterogeneous autoregressive model that approximates long-memory dynamics through mixed-frequency mean components. The new model accommodates heavy-tailed densities for returns and realised measures, ensuring robust updating for conditional variance process specified in a score-driven framework. This feature is essential when modelling long memory processes. The overall performance of the new model is better than that of the benchmark short-memory Realised GAS model. When comparing the performance of the two specifications of the new model, the empirical analysis results are dubious when considering different forecasting horizons. However, as expected, the fractionally integrated specification performs better for larger horizons than the other model specification.