## ARIMAX modeling

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Estimate the coefficients of an ARIMAX model

### Description

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

with the input data x passed through a difference filter D times. This difference filter is given by

where N denotes the length of x.
In the above formula, x denotes 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, i.e. the estimation error signal is returned.
Input parameters are

- order
`P` of the AR process,
- order
`Q` of the MA process,
- order
`R` of the eXtra / eXternal process and
- integral order
`D`.

The AR, MA and X coefficients , and of the estimated model will appear in the message window.

### Macro Synopsis

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

signal r,x,y,z;

int P,Q,R,D;

### Modules

Statistics

### Related Functions

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

### References

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