## ARMAX modeling

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

AR(MA)X model estimation

### Description

"ARMAX modeling" treats the given signals x, y, z as Auto-Regressive
Moving Average with eXtra / eXternal (ARMAX) process according to

where x is the input signal (usually a noise signal), y is the output signal and z is the extra / external input signal.
The model coefficients of the given orders are estimated and the residual
r (the estimation error) is returned. Input parameters are

- order P of the AR process,
- order Q of the MA process (choose Q=0 for an ARX model) and
- order R of the eXtra / eXternal process.

The ARMAX coefficients of the estimated model will appear in the
message window.
**Warning:** *Note that if the signals x and y have different x-axis scales (sampling periods), the signal with the largest scale will be adapted automatically by interpolating between successive sample points. The type of interpolation can be set in the Basic Options menu.*

### Macro Synopsis

`r = ARMAXmodel([x,y,z],P,Q,R);`

signal r,x,y,z;

int P,Q,R;

### Modules

Statistics

### Related Functions

AR simulation, ARIMA modeling,
ARIMAX modeling, ARMA model order,
ARMA modeling, ARMA simulation,
ARMA spectral density, ARMAX simulation,
NAR modeling, NARMA modeling.

### References

Ljung [10], Conover [11], Graybill
[12], Hollander/Wolfe [13]