[T,R,K,Z,H,D,U,Omg] = sspace(m,...)
m
[ model ] - Solved model object.T
[ numeric ] - Transition matrix.
R
[ numeric ] - Matrix at the shock vector in transition equations.
K
[ numeric ] - Constant vector in transition equations.
Z
[ numeric ] - Matrix mapping transition variables to measurement variables.
H
[ numeric ] - Matrix at the shock vector in measurement equations.
D
[ numeric ] - Constant vector in measurement equations.
U
[ numeric ] - Transformation matrix for predetermined variables.
Omg
[ numeric ] - Covariance matrix of shocks.
'triangular='
[ true
| false
] - If true, the state-space form returned has the transition matrix T
quasi triangular and the vector of predetermined variables transformed accordingly; this is the form used in IRIS calculations. If false, the state-space system refers to the original vector of transition variables.The state-space representation has the following form:
[xf;alpha] = T*alpha(-1) + K + R*e
y = Z*alpha + D + H*e
xb = U*alpha
Cov[e] = Omg
where xb
is an nb-by-1 vector of predetermined (backward-looking) transition variables and their auxiliary lags, xf
is an nf-by-1 vector of non-predetermined (forward-looking) variables and their auxiliary leads, alpha
is a transformation of xb
, e
is an ne-by-1 vector of shocks, and y
is an ny-by-1 vector of measurement variables. Furthermore, we denote the total number of transition variables, and their auxiliary lags and leads, nx = nb + nf.
The transition matrix, T
, is, in general, rectangular nx-by-nb. Furthremore, the transformed state vector alpha is chosen so that the lower nb-by-nb part of T
is quasi upper triangular.
You can use the get(m,'xVector')
function to learn about the order of appearance of transition variables and their auxiliary lags and leads in the vectors xb
and xf
. The first nf names are the vector xf
, the remaining nb names are the vector xb
.