forecast {KFAS}R Documentation

Forecast state space model

Description

Performs forecasting using output from function 'kf' (Kalman filter).

Usage

  forecast(out, fc=1, Zt.fc=NULL, Tt.fc=NULL, Rt.fc=NULL, Ht.fc=NULL, Qt.fc=NULL)

Arguments

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.

Details

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

Value

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)

[Package KFAS version 0.5.3 Index]