Estimate parameters of ARMAX model using time-domain data

```
sys = armax(data,[na
nb nc nk])
```

```
sys = armax(data,[na
nb nc nk],Name,Value)
```

`sys = armax(data,init_sys)`

`sys = armax(data,___,opt)`

returns an `sys`

= armax(`data`

,```
[na
nb nc nk]
```

)`idpoly`

model, `sys`

,
with estimated parameters and covariance (parameter uncertainties).
Estimates the parameters using the prediction-error method and specified
polynomial orders.

returns
an `sys`

= armax(`data`

,```
[na
nb nc nk]
```

,`Name,Value`

)`idpoly`

model, `sys`

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

pair
arguments.

Use the

`IntegrateNoise`

property to add integrators to the noise source.

An iterative search algorithm minimizes a robustified quadratic prediction error criterion. The iterations are terminated when any of the following is true:

Maximum number of iterations is reached.

Expected improvement is less than the specified tolerance.

Lower value of the criterion cannot be found.

You can get information about the stopping criteria using `sys.Report.Termination`

.

Use the `armaxOptions`

option set to create and configure options affecting
the estimation results. In particular, set the search algorithm attributes, such as
`MaxIterations`

and `Tolerance`

, using the
`'SearchOptions'`

property.

When you do not specify initial parameter values for the iterative search as an initial model, they are constructed in a special four-stage LS-IV algorithm.

The cutoff value for the robustification is based on the `Advanced.ErrorThreshold`

estimation option and on the estimated standard deviation of the residuals
from the initial parameter estimate. It is not recalculated during
the minimization. By default, no robustification is performed; the
default value of `ErrorThreshold`

option is 0.

To ensure that only models corresponding to stable predictors are tested, the algorithm performs a stability test of the predictor. Generally, both $$C(q)$$ and $$F(q)$$ (if applicable) must have all zeros inside the unit circle.

Minimization information is
displayed on the screen when the estimation option `'Display'`

is `'On'`

or `'Full'`

.
With `'Display'`

`='Full'`

, both
the current and the previous parameter estimates are displayed in
column-vector form, listing parameters in alphabetical order. Also,
the values of the criterion function (cost) are given and the Gauss-Newton
vector and its norm are also displayed. With ```
'Display' =
'On'
```

, only the criterion values are displayed.

`armax`

does not support continuous-time
model estimation. Use `tfest`

to
estimate a continuous-time transfer function model, or `ssest`

to estimate a continuous-time state-space
model.

`armax`

supports only time-domain data. For
frequency-domain data, use `oe`

to
estimate an Output-Error (OE) model.

Ljung, L. *System Identification: Theory for the User*,
Upper Saddle River, NJ: Prentice-Hall PTR, 1999. See chapter about
computing the estimate.

`aic`

| `armaxOptions`

| `arx`

| `bj`

| `forecast`

| `fpe`

| `goodnessOfFit`

| `iddata`

| `idfrd`

| `idpoly `

| `oe`

| `polyest`

| `ssest`

| `tfest`