We propose novel models for long memory dynamics in financial volatility and dependence for heavy-tailed data. For our purpose, we extend the short memory generalized autoregressive score models due to Creal, Koopman, and Lucas (2010) by adding a fractional order of integration. The key feature of both models is robustness to more extreme observations which might be critical in the long memory models, where the impact of innovations on the future values dissipates at the very slow rate.
Results from the empirical investigation for equity data indicate that the degree of memory in volatilities is similar across equities, while the degree of memory in correlations across pairs may be substantially different and different than the degree of memory in volatilities. The resulting model-based processes are related to high-frequency based realized measures and perform well compared to other competing standard models.