Asymmetric t -GARCH(1,1) Model for Heuristic Kalman Filtering

In this letter, the novel asymmetrict-GARCH(1,1) (ATGARCH(1,1)) model is proposed. By calculating the tail exponent (TE), it is discovered that the TE of the ATGARCH(1,1) distribution is smaller than the degree of freedom (dof) of its corresponding driving Student-t distribution. Actually, we get that the TE of the ATGARCH(1,1) distribution is jointly determined by the corresponding dof and its model parameters. Since the closed-form density functions of the ATGARCH(1,1) noises are unknown, the corresponding filtering problems are analyzed by the heuristic method. In the ATGARCH(1,1) noise cases, the simulation results show that our heuristic algorithm is superior to the standard Kalman filter (KF), the particle filter, and those robust KFs designed by the Student-t distribution models.