Momentary ARMA dependence
"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
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.
- Order P of the AR process
- Order Q of the MA process
- Adaptation time t for variance estimator (in x-axis
- 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.
The adaptation factor f usually lies below 0.05; t must not be
smaller than the input signal scale.
y = MomARMAdependence([x1,x2],P,Q,t,f,step);
Momentary ARMA bandpower, Momentary ARMA coherence,
Momentary ARMA spectrum,
Momentary bandpower, Momentary frequency,
Momentary mean, Momentary power.