## ARMA modeling

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Estimates the coefficients of an AR or an ARMA model

### Description

An Auto-Regressive (AR) process is defined
by

and an Auto-Regressive Moving Average (ARMA) process by

Here, r is a random process (or a noise signal).
"ARMA modeling" estimates the coefficients of an AR or an ARMA
process of given order for an input signal y using the Yule-Walker
and the Durbin approach, respectively.

Input parameters are

- order P of the AR process and
- order Q of the MA process (choose Q=0 for a pure AR model).

The coefficients of the estimated model will appear in the
message window. The signal returned is the residual signal r, i.e.
the estimation error signal.

### Macro Synopsis

`r = ARMAmodel(y,P,Q);`

signal r,y;

int P,Q;

### Modules

Statistics

### Related Functions

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

### References

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