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AR model estimation using instrumental variable method


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


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:


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


Estimation time series data.

data must be an iddata object with scalar output data only.


Order of the A polynomial


Order of the moving average process representing e(t).


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


Identified polynomial model.

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


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) + ...
miv = ivar(y,4);
mls = ar(y,4);


[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.

See Also

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Introduced before R2006a

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