# isnlarx

Detect nonlinearity in estimation data

## Syntax

## Description

`isnlarx(`

detects
nonlinearity in `data`

,`orders`

)`data`

by testing whether a nonlinear ARX
model with the indicated `orders`

produces a better estimate
of `data`

than a linear ARX model. The nonlinear model uses a
default `treepartition`

nonlinearity estimator.

The result of the test is printed to the Command Window and indicates whether a nonlinearity is detected. Use the printed detection ratio to assess the reliability of the nonlinearity detection test:

Larger values (

`>2`

) indicate that a significant nonlinearity was detected.Smaller values (

`<0.5`

) indicate that any error unexplained by the linear model is mostly noise. That is, no significant nonlinearity was detected.Values close to

`1`

indicate that the nonlinearity detection test is not reliable and that a weak nonlinearity may be present.

`isnlarx(___,`

specifies
additional nonlinear ARX model options using one or more `Name,Value`

)`Name,Value`

pair
arguments.

returns
the result of the nonlinearity test and suppresses the command window
output.`NLHyp`

= isnlarx(___)

`[`

additionally returns the test
quantities behind the evaluation.`NLHyp`

,`NLValue`

,`NLRegs`

,`NoiseSigma`

,`DetectRatio`

]
= isnlarx(___)

## Examples

## Input Arguments

## Output Arguments

## Algorithms

`isnlarx`

estimates a nonlinear ARX model
using the given data and a `treepartition`

nonlinearity
estimator.

The estimation data can be described as *Y*(*t*)
= *L*(*t*) + *F _{n}*(

*t*) +

*E*(

*t*), where:

*L*(*t*) is the portion of the data explained by the linear function of the nonlinear ARX model.*F*(_{n}*t*) is the portion of the data explained by the nonlinear function of the nonlinear ARX model. The output argument`NLValue`

is an estimate of the standard deviation of*F*(_{n}*t*). If the nonlinear function explains a significant portion of the data beyond the data explained by the linear function, a nonlinearity is detected.*E*(*t*) is the remaining error that is unexplained by the nonlinear ARX model and is typically white noise. The output argument`NoiseSigma`

is an estimate of the standard deviation of*E*(*t*).

## Version History

**Introduced in R2007a**