destmar

DESTMAR
Syntax
Description
Inputs
Outputs
Algorithm
Used By
See Also
References

DESTMAR

Fits a multivariable autoregressive model to a time-series.

Syntax

[Af,Ab,Sf,Sb] = destmar(v,d)

Description

This function fits a multivariable autoregressive model to a time-series v(k). The model-structure is

$v(k) = \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over e}(k) - \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over A}_1 v(k-1) - ... - \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over A}_d v(k-d)$

$v(k) = \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftharpoonup$}} \over e}(k) - \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftharpoonup$}} \over A}_1 v(k+1) - ... - \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftharpoonup$}} \over A}_d v(k+d)$

in which ef(k) and eb(k) are innovation sequences with covariance matrices Sf and Sb respectively. The fitting is performed according to [1].

Inputs

v is the time-series, a N x l matrix for a signal having N samples and which is l-dimensional.

d is the desired order d of the AR model.

Outputs

Af,Ab are the coefficient matrices Af and Ab of the causal and anticausal model.

Sf,Sb are the covariance matrices Sf and Sb of the causal and anticausal innovations.

Algorithm

A direct Hankel-matrix based estimation of the AR model is performed according to [1].

Used By

This is a top-level function that is used directly by the user.

References

[1] B. Davis, Parameter Estimation in Nonlinear Dynamical Systems with Correlated Noise. PhD thesis, Universite Catholique de Louvain-La-Neuve, Belgium, 2001.

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