## ARIMA modeling

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Estimate the coefficients of an ARIMA model

### Description

"ARIMA modeling" treats the given signal y as an Auto-Regressive
Integrated Moving Average (ARIMA) 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.
"ARIMA modeling" estimates its model coefficients of the given order and
returns the residual r, i.e. the estimation error signal.
Input parameters are

- order
`P` of the AR process,
- order
`Q` of the MA process and
- integral order
`D`.

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

### Macro Synopsis

`r = ARIMAmodel(y,P,Q,D);`

signal r,y;

int P,Q,D;

### Modules

Statistics

### Related Functions

AR simulation,
ARIMAX 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].