Assessing volatility persistence in fractional Heston models with self-exciting jumps

We derive a new fractional Heston model with self-exciting jumps. We study volatility persistence and demonstrate that the quadratic variation necessarily exhibits less memory than the integrated variance, which preserves the degree of long-memory of the instantaneous volatility. Focusing on realized volatility measures, we find that traditional long-memory estimators are dramatically downward biased, in particular for low-frequency intraday sampling. Conveniently, our Monte Carlo experiments reveal that some noise-robust local Whittle-type estimators offer good finite sample properties. We apply our theoretical results in a risk forecasting study and show that our frequency-domain forecasting procedure outperforms the traditional benchmark models.