AR model estimation using instrumental variable method
sys = ivar(data,na)
sys = ivar(data,na,nc)
sys = ivar(data,na,nc,max_size)
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
nc, possibly time varying.
assumed to be equal to
na. Instruments are chosen
as appropriately filtered outputs, delayed
Estimation time series data.
Order of the A polynomial
Order of the moving average process representing e(t).
Maximum matrix size.
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) + ... 0.2*randn(500,1),); miv = ivar(y,4); mls = ar(y,4); spectrum(miv,mls)
 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.