I understand that the steady-state Kalman filter is more computationally efficient because the noise in a measurement equation and the shock in a state equation have a constant variance over the time period. However, what model should I use if I want to study the effect of a noise shock, which refers to a large shock that was not imaginable?
Should I use a time-varying Kalman filter that allows for the variance of noise to vary? I am faced with this question because I cannot exactly tell the differences between these models and their respective advantages and disadvantages. Please help me out.