diffuse filter: removed special treatment of static variables
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383d891e81
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2f9dc09285
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@ -52,20 +52,8 @@ function [Z,ST,R1,QT,Pstar,Pinf] = schur_statespace_transformation(mf,T,R,Q,qz_c
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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np = size(T,1);
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if nargin == 6,
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indx = restrict_columns;
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indx0=find(~ismember([1:np],indx));
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else
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indx=(find(max(abs(T))>0));
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indx0=(find(max(abs(T))==0));
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end
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T0=T(indx0,indx); %static variables vs. dynamic ones
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R0=R(indx0,:); % matrix of shocks for static variables
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% perform Kitagawa transformation only for non-zero columns of T
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T=T(indx,indx);
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R=R(indx,:);
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np = size(T,1);
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% perform Kitagawa transformation
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[QT,ST] = schur(T);
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e1 = abs(ordeig(ST)) > 2-qz_criterium;
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[QT,ST] = ordschur(QT,ST,e1);
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@ -73,7 +61,9 @@ k = find(abs(ordeig(ST)) > 2-qz_criterium);
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nk = length(k);
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nk1 = nk+1;
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Pstar = zeros(np,np);
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B = QT'*R*Q*R'*QT;
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R1 = QT'*R;
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B = R1*Q*R1';
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% computes variance of stationary block (lower right)
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i = np;
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while i >= nk+2
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if ST(i,i-1) == 0
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@ -113,47 +103,20 @@ if i == nk+1
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c = ST(nk+1,:)*(Pstar(:,nk+2:end)*ST(nk1,nk+2:end)')+ST(nk1,nk1)*ST(nk1,nk+2:end)*Pstar(nk+2:end,nk1);
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Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
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end
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R1 = QT'*R;
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ST1=ST;
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% now I recover stationarized static variables
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% using
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% ss = s-z and
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% z-z(-1) (growth rates of unit roots) only depends on stationary variables
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np0=length(indx0);
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Pstar = blkdiag(zeros(np0),Pstar);
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ST = [zeros(length(Pstar),length(indx0)) [T0*QT ;ST]];
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R1 = [R0; R1];
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ST0=ST;
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ST0(:,1:np0+nk)=0;
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ST0(np0+1:np0+nk,:)=0;
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ST0(1:np0,np0+nk+1:end) = ST(1:np0,np0+nk+1:end)-ST(1:np0,np0+1:np0+nk)*ST(np0+1:np0+nk,np0+nk+1:end);
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R10 = R1;
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R10(np0+1:np0+nk,:)=0;
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R10(1:np0,:) = R1(1:np0,:)-ST(1:np0,np0+1:np0+nk)*R1(np0+1:np0+nk,:);
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Pstar = ...
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ST0*Pstar*ST0'+ ...
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R10*Q*R10';
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QT = blkdiag(eye(np0),QT);
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QT(1:np0,np0+1:np0+nk) = QT(1:np0,np0+1:np0+nk)+ST(1:np0,np0+1:np0+nk);
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% reorder QT entries
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QT([indx0(:); indx(:)],:) = QT;
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Z = QT(mf,:);
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ST(1:np0,:) = ST0(1:np0,:);
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R1(1:np0,:) = R10(1:np0,:);
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% stochastic trends with no influence on observed variables are
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% arbitrarily initialized to zero
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Pinf = zeros(np,np);
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Pinf(1:nk,1:nk) = eye(nk);
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[QQ,RR,EE] = qr(Z*ST(:,1+np0:nk+np0),0);
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k = find(abs(diag([RR; zeros(nk-size(Z,1),size(RR,2))])) < 1e-8);
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[QQ,RR,EE] = qr(Z*ST,0);
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k = find(abs(diag(RR)) < 1e-8);
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if length(k) > 0
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k1 = EE(:,k);
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dd =ones(nk,1);
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dd(k1) = zeros(length(k1),1);
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Pinf(1:nk,1:nk) = diag(dd);
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end
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Pinf = blkdiag(zeros(np0),Pinf);
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