AR model estimation using instrumental variable method
sys = ivar(data,na)
sys = ivar(data,na,nc)
sys = ivar(data,na,nc,max_size)
estimates
an AR polynomial model, sys
= ivar(data
,na
)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.
specifies
the value of the moving average process order, sys
= ivar(data
,na
,nc
)nc
,
separately.
specifies
the maximum size of matrices formed during estimation.sys
= ivar(data
,na
,nc
,max_size
)

Estimation time series data.


Order of the A polynomial 

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

Maximum matrix size.
Specify Default: 250000 

Identified polynomial model.

Compare spectra for sinusoids in noise, estimated by the IV method and by the forwardbackward 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)
[1] Stoica, P., et al. Optimal Instrumental Variable Estimates of the ARparameters of an ARMA Process, IEEE Trans. Autom. Control, Volume AC30, 1985, pp. 1066–1074.