Mohammad Mohammadi - Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
Saeid Rezakhah - Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran,
Navideh Modarresi - Faculty of Statistics, Mathematics and Computer, Allameh Tabataba'i University, Tehran, Iran

The intra-day return of high-frequency financial data have periodic structure. These data have volatilities and existing works assumes it is a stationary process. However, there is evidence for the presence of intra-day periodicity or seasonality in volatility. Due to the inherent periodicity and non-linear characteristics of high-frequency data, the accurate prediction of these data is critical to the market activity. In order to present a model that supports this feature, we introduce a hybrid semi Lévy driven continuous-time ARMA (SLCARMA)-gate recurrent unit neural network (GRUNN) model. The hybrid SLCARMA-GRUNN model based on the traditional method that assume the linear components and non-linear components should be linearly added.The proposed hybrid model is applied to ۳۰-minute squared log returns of Dow Jones Industrial Average indices

CARMA model, Gated recurrent unit neural network, Kalman filter, Periodically correlated process, Recurrent neural networks, Semi-Lévy process.