Abstract: Aiming at  the problem that the traditional EGARCH model was difficult to capture long-term memory, we proposed an  fBm-EGARCH model by introducing fractional Brownian motion. We gave the second-order moment, the fourth-order moment and covariance function properties of the model, and   theoretically  proved its long-term memory. Numerical simulation results show that the model can not only accurately capture short-term fluctuations, but also reflect long-term memory, which verifies the effectiveness of the model.

Key words: EGARCH model, fractional Brownian motion,  , long-term memory, liquidity