News shocks and Kalman filter

General DSGE Modeling
1

Dear dynare users,

I do not fully understand how news shocks affect endogenous variables before materialize.
Imagine that I have a news shock observed 4 periods before realizing. When does this shock enter Kalman filter?.
As far as I understand, the kalman filter generates a projection of the model variables at t given the state variables at t-1 and the shocks at t. Nevertheless, this news shock is realized at time t-4.
Therefore, is this shock entering in the kalman filter in time t-4?

Could someone share any paper where this is explained?

Thanks in advance for any help!

2

News shocks result in an augmented state vector. So once the shock is known, there is a state variable keeping track of it until it finally materializes.

3

First, thank you very much for your quick answer professor Pfeifer.

Just to clarify, the shock is known in t-4 and therefore it enters in the kalman filter in time t-4 and after that there is an state variable (that i guess is constructed through auxiliary variables) in each t-3, t-2, t-1 and t. Is that right?

For example, in this case:
aux_4=aux_3(-1);
aux_3=aux_2(-1);
aux_2=aux_1(-1);
aux_1=aux_0(-1);
aux_0=news4;

news4 enters in kalman filter at time t, aux_1 enters at time t-1 … aux_4 enters at time t-4

4

Yes, exactly. Dynare does that part automatically.