solutionMatrices (Model)
Access first-order state-space (solution) matrices
Syntax
output = solutionMatrices(model, ...)
Input Arguments
model [ Model ]
Solved model object.
Output Arguments
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.
Options
Triangular=true [ 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 default form used in IRIS calculations. If
false, the state-space system is based on the original vector of
transition variables.
Description
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, 'xiVector') 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.