Documentation of iv

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Function Synopsis

TH=iv(z,nn,NF,MF,maxsize,T,p)

Help text

IV     Computes instrumental variable estimates for single output ARX-models.

   TH = iv(Z,NN,NF,MF)

   TH: returned as the IV-estimate of the ARX-model
   A(q) y(t) = B(q) u(t-nk) + v(t)
   along with relevant structure information. See HELP THETA for
   the exact structure of TH.

   Z : the output-input data Z=[y u], with y and u as column vectors.
   For multi-input systems u=[u1 u2 ... un]

   NN: NN=[na nb nk] gives the orders and delays associated with the
   above model.
   NF and MF define the instruments X as
   NF(q) x(t) = MF(q) u(t)

   See IV4 for good, automatic choices of instruments.

   TH=iv(Z,NN,NF,MF,maxsize,T)
   allows access to some parameters associated with the algorithm.
   See HELP AUXVAR for an explanation of these.

Cross-Reference Information

Listing of function iv

function TH=iv(z,nn,NF,MF,maxsize,T,p)

%   L. Ljung 10-1-86
%   Copyright (c) 1986-98 by The MathWorks, Inc.
%   $Revision: 2.3 $  $Date: 1997/12/02 03:43:46 $

[Ncap,nz]=size(z); nu=nz-1;
na=nn(1);nb=nn(2:1+nu);nk=nn(2+nu:1+2*nu);n=na+sum(nb);
%
% *** Some initial tests on the input arguments ***
maxsdef=idmsize(Ncap,n);

if nargin<7, p=1;end
if nargin<6, T=1;end
if nargin<5, maxsize=maxsdef;end
if T<0,T=1;end,if maxsize<0,maxsize=maxsdef;end
if isempty(T), T=1;end,if isempty(maxsize),maxsize=maxsdef;end
% *** construct instruments (see (7.111)-(7.112)) ***

     x=zeros(Ncap,1);
     for k=1:nu
         x=x+filter(MF(k,:),NF,z(:,k+1));
     end
%

TH=ivx(z,nn,x,maxsize,T,p);
if p~=0,TH(2,7)=3;end