40 lines
972 B
Matlab
40 lines
972 B
Matlab
% [a,ia,js] = SPBuild_a(h,qcols,neq)
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%
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% Build the companion matrix, deleting inessential lags.
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% Solve for x_{t+nlead} in terms of x_{t+nlag},...,x_{t+nlead-1}.
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function [a,ia,js] = SPBuild_a(h,qcols,neq)
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left = 1:qcols;
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right = qcols+1:qcols+neq;
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hs=SPSparse(h);
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hs(:,left) = -hs(:,right)\hs(:,left);
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% Build the big transition matrix.
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a = zeros(qcols,qcols);
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if(qcols > neq)
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eyerows = 1:qcols-neq;
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eyecols = neq+1:qcols;
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a(eyerows,eyecols) = eye(qcols-neq);
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end
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hrows = qcols-neq+1:qcols;
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a(hrows,:) = hs(:,left);
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% Delete inessential lags and build index array js. js indexes the
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% columns in the big transition matrix that correspond to the
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% essential lags in the model. They are the columns of q that will
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% get the unstable left eigenvectors.
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js = 1:qcols;
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zerocols = sum(abs(a)) == 0;
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while( any(zerocols) )
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a(:,zerocols) = [];
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a(zerocols,:) = [];
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js(zerocols) = [];
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zerocols = sum(abs(a)) == 0;
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end
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ia = length(js);
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