Estimate parameters of ARX, ARIX, AR, or ARI model

specifies additional options using one or more name-value pair arguments. For instance,
using the name-value pair argument `sys`

= arx(`data`

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

,`Name,Value`

)`'IntegrateNoise',1`

estimates an ARIX or ARI
structure model, which is useful for systems with nonstationary disturbances.

specifies estimation options using the option set `sys`

= arx(`data`

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

,___,`opt`

)`opt`

. Specify
`opt`

after all other input arguments.

QR factorization solves the overdetermined set of linear equations that constitutes the least-squares estimation problem.

Without regularization, the ARX model parameters vector θ is estimated by solving the normal equation

$$\left({J}^{T}J\right)\theta ={J}^{T}y$$

where *J* is the regressor matrix and *y* is
the measured output. Therefore,

$$\theta ={\left({J}^{T}J\right)}^{-1}{J}^{T}y$$

Using regularization adds the regularization term

$$\theta ={\left({J}^{T}J+\lambda R\right)}^{-1}{J}^{T}y$$

where λ and R are the regularization constants. For more information on the regularization
constants, see `arxOptions`

.

When the regression matrix is larger than the `MaxSize`

specified in
`arxOptions`

, the data is segmented and QR factorization is performed iteratively
on the data segments.