- #1
spirall
- 2
- 0
Hi all,
I have a standard local level model, but the disturbances are not independent:
y_t=μ_t+ε_t, μ_t+1=μ_t+η_t, E(ε_t η_t) =/= 0
In order to derive the Kalman filter, I rewrite this model in state space form
y_t=Z_t α_t+ε_t, ε_t~NID(0,H_t ),
α_(t+1)=T_t α_t+R_t η_t, η_t~NID(0,Q_t ),
α_1~N(a_1,P_1 ),
α_t=[μ_t
ξ_t ]
Z_t=[1 1],
H_t=0,
Q_t=[σ_η^2 σ_ξη
σ_ξη σ_ξ^2 ],
T_t=[1 0
0 0],
R_t=[1 0
0 1],
η_t=[η_t
ξ_(t+1)].
I wonder whether there is any difference in the derivation of the Kalman filter, since the matrix Q in not diagonal.
Thank you
I have a standard local level model, but the disturbances are not independent:
y_t=μ_t+ε_t, μ_t+1=μ_t+η_t, E(ε_t η_t) =/= 0
In order to derive the Kalman filter, I rewrite this model in state space form
y_t=Z_t α_t+ε_t, ε_t~NID(0,H_t ),
α_(t+1)=T_t α_t+R_t η_t, η_t~NID(0,Q_t ),
α_1~N(a_1,P_1 ),
α_t=[μ_t
ξ_t ]
Z_t=[1 1],
H_t=0,
Q_t=[σ_η^2 σ_ξη
σ_ξη σ_ξ^2 ],
T_t=[1 0
0 0],
R_t=[1 0
0 1],
η_t=[η_t
ξ_(t+1)].
I wonder whether there is any difference in the derivation of the Kalman filter, since the matrix Q in not diagonal.
Thank you