forecast {KFAS} | R Documentation |
Performs forecasting using output from function 'kf' (Kalman filter).
forecast(out, fc=1, Zt.fc=NULL, Tt.fc=NULL, Rt.fc=NULL, Ht.fc=NULL, Qt.fc=NULL)
out |
Output from function 'kf'. |
fc |
Integer which states how many observations is forecasted. |
Zt.fc |
In case where matrix Z is not time-invariant, p*m*fc array of matrix Zt, t=n+1,...,n+fc. |
Tt.fc |
In case where matrix T is not time-invariant, m*m*fc array of matrix Tt, t=n+1,...,n+fc. |
Rt.fc |
In case where matrix R is not time-invariant, m*r*fc array of matrix Rt, t=n+1,...,n+fc. |
Ht.fc |
In case where matrix H is not time-invariant, p*p*fc array of matrix Ht, t=n+1,...,n+fc. |
Qt.fc |
In case where matrix Q is not time-invariant, r*r*fc array of matrix Qt, t=n+1,...,n+fc. |
The state space model is given by
y_t = Z_t * alpha_t + eps_t (observation equation)
alpha_t+1 = T_t * alpha_t + R_t * eta_t(transition equation)
where eps_t ~ N(0,H_t) and eta_t ~ N(0,Q_t)
Dimensions of variables are:
'yt' p*n
'Zt' p*m or p*m*n
'Tt' m*m or m*m*n
'Rt' m*r or m*r*n
'Ht' p*p or p*p*n
'Qt' r*r or r*r*n
A list with the following elements:
yt.fc |
p*fc array of forecasts of observations. |
Ft.fc |
p*p*fc array of mean square error matrix |
at.fc |
m*(fc+1) array of E(alpha_t | y_1, y_2, ... , y_n) |
Pt.fc |
m*m*(fc+1) array of Var(alpha_t | y_1, y_2, ... , y_n) |