## ARMA dependence

Purpose

Description

Tips

Macro Synopsis

Modules

Related Functions

### Purpose

Momentary ARMA dependence

### Description

"ARMA dependence" is an adaptive ARMA filter for
the momentary estimation of the degree of dependence from a
bivariate ARMA model Y with time-varying parameters

with being the matrices of autoregressive
(AR) parameters and being the matrices of
the moving average (MA) parameters. Z denotes a two-dimensional
noise process.
The momentary ARMA dependence is given by

This degree equals zero in the case of independent components and
increases with a higher synchronisation of the components.
The recursive estimation of the model coefficients is done
adaptively where the adaption speed can be adjusted by the choice of
the parameters f and t (see below). By increasing f and decreasing
t, a quicker reaction of the estimation procedure is possible after
rapid structure changes, but will also lead to an estimation
sequence that is less smooth and tends to be less robust.

Parameters are

- Order P of the AR process
- Order Q of the MA process
- Adaptation time t for variance estimator (in x-axis
units)
- Adaptation factor f for parameter estimation (see also Momentary ARMA coherence)
- Time interval
`step` (in samples) on the x-axis between two successive computations of the dependence.

**Warning:** *Note that if the input signals 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.*

### Tips

The adaptation factor f usually lies below 0.05; t must not be
smaller than the input signal scale.

### Macro Synopsis

`y = MomARMAdependence([x1,x2],P,Q,t,f,step);`

signal x1,x2,y;

int P,Q;

float t,f;

int step;

### Modules

Nonlinear

### Related Functions

Momentary ARMA bandpower, Momentary ARMA coherence,
Momentary ARMA spectrum,
Momentary bandpower, Momentary frequency,
Momentary mean, Momentary power.