ivar

AR model estimation using instrumental variable method

Syntax

sys = ivar(data,na) sys = ivar(data,na,nc) sys = ivar(data,na,nc,max_size)

Description

sys = ivar(data,na) estimates an AR polynomial model, sys, using the instrumental variable method and the time series data data. na specifies the order of the A polynomial.

An AR model is represented by the equation:

$A (q) y (t) = e (t)$

In the above model, e(t) is an arbitrary process, assumed to be a moving average process of order nc, possibly time varying. nc is assumed to be equal to na. Instruments are chosen as appropriately filtered outputs, delayed nc steps.

sys = ivar(data,na,nc) specifies the value of the moving average process order, nc, separately.

sys = ivar(data,na,nc,max_size) specifies the maximum size of matrices formed during estimation.

Input Arguments

`data`	Estimation time series data. `data` must be an `iddata` object with scalar output data only.
`na`	Order of the A polynomial
`nc`	Order of the moving average process representing e(t).
`max_size`	Maximum matrix size. `max_size` specifies the maximum size of any matrix formed by the algorithm for estimation. Specify `max_size` as a reasonably large positive integer. Default: 250000

Output Arguments

sys

Identified polynomial model.

sys is an AR idpoly model which encapsulates the identified polynomial model.

Examples

Compare spectra for sinusoids in noise, estimated by the IV method and by the forward-backward least squares method.

y = iddata(sin([1:500]'*1.2) + sin([1:500]'*1.5) + ...
           0.2*randn(500,1),[]);
miv = ivar(y,4);
mls = ar(y,4);
spectrum(miv,mls)

References

[1] Stoica, P., et al. Optimal Instrumental Variable Estimates of the AR-parameters of an ARMA Process, IEEE Trans. Autom. Control, Volume AC-30, 1985, pp. 1066–1074.

Documentation