`disp(`

displays
summary information for the state-space model (`Mdl`

)`ssm`

) `Mdl`

. The display includes
the state and observation equations as a system of scalar equations
to facilitate model verification. The display also includes the coefficient
dimensionalities, notation, and initial state distribution types.

The software displays unknown parameter values using `c1`

for
the first unknown parameter, `c2`

for the second
unknown parameter, and so on.

For time-varying models, if there are more than 20 different sets of equations, then the software displays the first and last 10 groups in terms of time (the last group is the latest).

`disp(___,`

displays
the `Name,Value`

)`ssm`

model with additional options specified
by one or more `Name,Value`

pair arguments. For
example, specify the number of digits to display after the decimal
point for model coefficients, or the number of terms per row for state
and observation equations.

The software always displays explicitly specified state-space models (that is, models you create without using a parameter-to-matrix mapping function). Try explicitly specifying state-space models first so that you can verify them using

`disp`

.A parameter-to-matrix function that you specify to create

`Mdl`

is a black box to the software. Therefore, the software might not display complex, implicitly defined state-space models.

A *state-space model* is
a discrete-time, stochastic model that contains two sets of equations:

One describing how a latent process transitions in time (the

*state equation*)Another describing how an observer measures the latent process at each period (the

*observation equation*)

Symbolically, you can write a linear, multivariate, Gaussian state-space model using the following system of equations

$$\begin{array}{l}{x}_{t}={A}_{t}{x}_{t-1}+{B}_{t}{u}_{t}\\ {y}_{t}-{Z}_{t}\beta ={C}_{t}{x}_{t}+{D}_{t}{\epsilon}_{t},\end{array}$$

for *t* = 1,...,*T*.

$${x}_{t}=\left[{x}_{t1},\mathrm{...},{x}_{t{m}_{t}}\right]\prime $$ is an

*m*-dimensional state vector describing the dynamics of some, possibly unobservable, phenomenon at period_{t}*t*.$${y}_{t}=\left[{y}_{t1},\mathrm{...},{y}_{t{n}_{t}}\right]\prime $$ is an

*n*-dimensional observation vector describing how the states are measured by observers at period_{t}*t*.*A*is the_{t}*m*-by-_{t}*m*_{t – 1}state-transition matrix describing how the states at time*t*transition to the states at period*t*– 1.*B*is the_{t}*m*-by-_{t}*k*state-disturbance-loading matrix describing how the states at period_{t}*t*combine with the innovations at period*t*.*C*is the_{t}*n*-by-_{t}*m*measurement-sensitivity matrix describing how the observations at period_{t}*t*relate to the states at period*t*.*D*is the_{t}*n*-by-_{t}*h*observation-innovation matrix describing how the observations at period_{t}*t*combine with the observation errors at period*t*.The matrices

*A*,_{t}*B*,_{t}*C*, and_{t}*D*are referred to as_{t}*coefficient matrices*, and might contain unknown parameters.$${u}_{t}=\left[{u}_{t1},\mathrm{...},{u}_{t{k}_{t}}\right]\prime $$ is a

*k*-dimensional, Gaussian, white-noise, unit-variance vector of state disturbances at period_{t}*t*.$${\epsilon}_{t}=\left[{\epsilon}_{t1},\mathrm{...},{\epsilon}_{t{h}_{t}}\right]\prime $$ is an

*h*-dimensional, Gaussian, white-noise, unit-variance vector of observation innovations at period_{t}*t*.*ε*and_{t}*u*are uncorrelated._{t}For time-invariant models,

$${Z}_{t}=\left[\begin{array}{cccc}{z}_{t1}& {z}_{t2}& \cdots & {z}_{td}\end{array}\right]$$ is row

*t*of a*T*-by-*d*matrix of predictors*Z*. Each column of*Z*corresponds to a predictor, and each successive row to a successive period. If the observations are multivariate, then all predictors deflate each observation.*β*is a*d*-by-*n*matrix of regression coefficients for*Z*._{t}

To write a time-invariant state-space model, drop the *t* subscripts
of all coefficient matrices and dimensions.

If you implicitly created

`Mdl`

using`ssm`

, and if the software cannot infer locations for unknown parameters from the parameter-to-matrix function, then the software evaluates these parameters using their initial values and displays them as numerical values. For example, this happens when, for example, there is a random, unknown coefficient in the parameter-to-matrix function, which is a convenient form for a Monte Carlo study.The software always displays the initial state distributions as numerical values because, in many cases, the initial distribution depends on the values of the state equation matrices

`A`

and`B`

, which might be a complicated function of unknown parameters. In such situations, the software does not display the initial distribution symbolically, and, if`Mean0`

and`Cov0`

contain unknown parameters, then the software evaluates and displays numerical values for the unknown parameters.

[1] Durbin J., and S. J. Koopman. *Time Series
Analysis by State Space Methods*. 2nd ed. Oxford: Oxford
University Press, 2012.

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