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function [vd,str,imf] = errors(Bh,swish,nn)
% Computing variance decompositions and impulse functions with
% [vd,str,imf] = errors(Bh,swish,nn)
% where imf and vd is of the same format as in RATS, that is to say:
% Column: nvar responses to 1st shock,
% nvar responses to 2nd shock, and so on.
% Row: steps of impulse responses.
% vd: variance decompositions
% str: standard errors of each variable, steps-by-nvar
% imf: impulse response functions
% Bh is the estimated reduced form coefficient in the form
% Y(T*nvar) = XB + U, X: T*k, B: k*nvar. The matrix
% form or dimension is the same as "Bh" from the function "sye";
% swish is the inv(A0) in the structural model A(L)y(t) = e(t).
% nn is the numbers of inputs [nvar,lags,# of impulse responses].
%
% Copyright (C) 1997-2012 Tao Zha
%
% This free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% It is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% If you did not received a copy of the GNU General Public License
% with this software, see <http://www.gnu.org/licenses/>.
%
nvar = nn(1);
lags = nn(2);
imstep = nn(3); % number of steps for impulse responses
Ah = Bh';
% Row: nvar equations
% Column: 1st lag (with nvar variables) to lags (with nvar variables) + const = k.
imf = zeros(imstep,nvar*nvar);
vd = imf;
% Column: nvar responses to 1st shock, nvar responses to 2nd shock, and so on.
% Row: steps of impulse responses.
str = zeros(imstep,nvar); % initializing standard errors of each equation
M = zeros(nvar*(lags+1),nvar);
% Stack lags M's in the order of, e.g., [Mlags, ..., M2,M1;M0]
M(1:nvar,:) = swish';
Mtem = M(1:nvar,:); % temporary M -- impulse responses.
%
Mvd = Mtem.^2; % saved for the cumulative sum later
Mvds = (sum(Mvd'))';
str(1,:) = sqrt(Mvds'); % standard errors of each equation
Mvds = Mvds(:,ones(size(Mvds,1),1));
Mvdtem = (100.0*Mvd) ./ Mvds; % tempoary Mvd -- variance decompositions
% first or initial responses to
% one standard deviation shock (or forecast errors).
% Row: responses; Column: shocks
%
% * put in the form of "imf"
imf(1,:) = Mtem(:)';
vd(1,:) = Mvdtem(:)';
t = 1;
ims1 = min([imstep-1 lags]);
while t <= ims1
Mtem = Ah(:,1:nvar*t)*M(1:nvar*t,:);
% Row: nvar equations, each for the nvar variables at tth lag
M(nvar+1:nvar*(t+1),:)=M(1:nvar*t,:);
M(1:nvar,:) = Mtem;
% ** impulse response functions
imf(t+1,:) = Mtem(:)';
% stack imf with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
% ** variance decompositions
Mvd = Mvd + Mtem.^2; % saved for the cumulative sum later
Mvds = (sum(Mvd'))';
str(t+1,:) = sqrt(Mvds'); % standard errors of each equation
Mvds = Mvds(:,ones(size(Mvds,1),1));
Mvdtem = (100.0*Mvd) ./ Mvds; % tempoary Mvd -- variance decompositions
vd(t+1,:) = Mvdtem(:)';
% stack vd with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
t= t+1;
end
for t = lags+1:imstep-1
Mtem = Ah(:,1:nvar*lags)*M(1:nvar*lags,:);
% Row: nvar equations, each for the nvar variables at tth lag
M(nvar+1:nvar*(t+1),:) = M(1:nvar*t,:);
M(1:nvar,:)=Mtem;
% ** impulse response functions
imf(t+1,:) = Mtem(:)';
% stack imf with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
% ** variance decompositions
Mvd = Mvd + Mtem.^2; % saved for the cumulative sum later
Mvds = (sum(Mvd'))';
str(t+1,:) = sqrt(Mvds'); % standard errors of each equation
Mvds = Mvds(:,ones(size(Mvds,1),1));
Mvdtem = (100.0*Mvd) ./ Mvds; % tempoary Mvd -- variance decompositions
vd(t+1,:) = Mvdtem(:)';
% stack vd with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
end
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