IRIS Toolbox Reference Manual

## sspace

State-space matrices describing the model solution

#### Syntax

    [T,R,K,Z,H,D,U,Omg] = sspace(m,...)

#### Input arguments

- `m` [ 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` | `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.

#### 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,'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`.

IRIS Toolbox. Copyright © 2007—2013 Jaromir Benes.