Bayesian the Kalman Type Recursive Formulae

In this paper, the Kalman filter for a variance term of state space models is derived. First, it is assumed that the innovation term of state space model have a GARCH structure and the Kalman filter is derived. Then, it is assumed that the error term of observation equation is GARCH and the Kalman filtering is surveyed. Finally, considering an inverse gamma prior distribution for variance of observation equation again the Kalman filter is proposed. A numerical example is also given. Finally a conclusion section is presented.