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function [residuals, info] = calibrateresiduals(dbase, info, M_)
% [residuals, info] = calibrateresiduals(dbase, info, M_)
% Compute residuals in a backward model. Residuals are unobserved exogenous
% variables appearing additively in equations and without lags. An equation
% cannot have more than one residual, and a residual cannot appear in more
% than one equation.
%
% INPUTS
% - dbase [dseries] Object containing all the endogenous and observed exogenous variables.
% - info [struct] Informations about the residuals.
% - M_ [struct] M_ as produced by the preprocessor.
%
% OUTPUTS
% - residuals [dseries] Object containing the identified residuals.
% - info [struct] Informations about the residuals.
%
% REMARKS
% The first two input arguments are the output of checkdatabaseforinversion
% routine.
% Copyright © 2017-2023 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is 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.
%
% Dynare 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.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
displayresidualsequationmapping = false;
% Get function handle for the dynamic model
dynamic_resid = str2func([M_.fname,'.sparse.dynamic_resid']);
% Get data for all the endogenous variables.
ydata = dbase{info.endonames{:}}.data;
% Define function to retrieve an equation name
eqname = @(z) M_.equations_tags{cellfun(@(x) x==z, M_.equations_tags(:,1)) & cellfun(@(x) isequal(x, 'name'), M_.equations_tags(:,2)),3};
% Get data for all the exogenous variables. Missing exogenous variables, to be solved for, have NaN values.
exogenousvariablesindbase = intersect(info.exonames, dbase.name);
residuals = dseries(NaN(dbase.nobs, length(info.residuals)), dbase.init, info.residuals);
allexogenousvariables = [dbase{exogenousvariablesindbase{:}}, residuals];
allexogenousvariables = allexogenousvariables{info.exonames{:}};
xdata = allexogenousvariables.data;
% Evaluate the dynamic equation
n = size(ydata, 2);
y = [ydata(1,:)'; ydata(2,:)'; NaN(n, 1)];
r = dynamic_resid(y, xdata(2,:), M_.params, zeros(n, 1));
% Check that the number of equations evaluating to NaN matches the number of residuals
idr = find(isnan(r));
if ~isequal(length(idr), residuals.vobs)
error('Each residual should appear in only one equation, and an equation cannot have more than one residual!')
end
% Check that the non NaN equations have zero residuals (model and data consistency).
ido = setdiff(1:n, idr);
if ~isempty(find(abs(r(ido))>1e-6))
disp('Provided data and model are not consistent in equations:')
idx = find(abs(r)>1e-6);
c1 = 'Equation';
c1 = strvcat(c1, '--------');
for i = 1:length(idx)
c1 = strvcat(c1, sprintf(' %s', num2str(idx(i))));
end
c2 = 'Residual';
c2 = strvcat(c2, '--------');
for i = 1:length(idx)
c2 = strvcat(c2, sprintf('%s', num2str(r(idx(i)))));
end
c2 = strvcat(c2(1, :), repmat('-', 1, size(c2, 2)), c2(3:end,:));
c5 = 'Equation name';
c5 = strvcat(c5, '-------------');
for i = 1:length(idx)
c5 = strvcat(c5, sprintf(' %s', eqname(idx(i))));
end
c3 = repmat(' | ', size(c2, 1), 1);
c4 = repmat(' ', size(c2, 1), 1);
cc = [c4, c1, c3, c2, c3, c5];
skipline()
disp(cc)
skipline()
disp('Please check model and dataset.')
end
% Associate the residuals with equations equations evaluating to NaNs.
info.equations = cell(residuals.vobs, 1);
info.residualindex = cell(residuals.vobs, 1);
for i = 1:residuals.vobs
residualname = residuals.name{i};
info.residualindex(i) = {strmatch(residualname, allexogenousvariables.name, 'exact')};
tmpxdata = xdata;
tmpxdata(2, info.residualindex{i}) = 0;
r = dynamic_resid(y, tmpxdata(2,:), M_.params, zeros(n, 1));
info.equations(i) = { idr(find(~isnan(r(idr))))};
end
if displayresidualsequationmapping
c1 = 'Residual';
for i=1:length(info.residuals)
c1 = strvcat(c1, sprintf('%s', info.residuals{i}));
end
c1 = strvcat(c1(1,:), repmat('-', 1, size(c1, 2)), c1(2:end,:));
c2 = 'Equation';
for i=1:length(info.residuals)
c2 = strvcat(c2, sprintf(' %s', num2str(info.equations{i})));
end
c2 = strvcat(c2(1,:), repmat('-', 1, size(c2, 2)), c2(2:end,:));
c3 = repmat(' | ', size(c2, 1), 1);
c4 = repmat(' ', size(c2, 1), 1);
cc = [c4, c1, c3, c2];
skipline()
disp(cc)
skipline()
end
% Compute residuals
xdata(:,cell2mat(info.residualindex)) = 0;
rdata = NaN(residuals.nobs, residuals.vobs);
for t=2:size(xdata, 1)
y = [ydata(t-1,:)'; ydata(t,:)'; NaN(n, 1)];
r = dynamic_resid(y, xdata(t,:), M_.params, zeros(n, 1));
rdata(t,:) = transpose(r(cell2mat(info.equations)));
end
residuals = dseries(rdata, dbase.init, info.residuals);
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