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function [A0, AR, B] = get_companion_matrix_legacy(auxiliary_model_name, auxiliary_model_type)
% Gets the companion VAR representation of a PAC auxiliary model.
% Depending on the nature of this auxiliary model the output is
% saved in oo_.{var,trend_component}.(auxiliary_model_name).CompanionMatrix
%
% INPUTS
% - auxiliary_model_name [string] the name of the auxiliary model
% - auxiliary_model_type [string] the type of the auxiliary model
% ('var' or 'trend_component')
%
% OUTPUTS
% - None
% Copyright © 2018 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/>.
global oo_ M_
if nargin<2
if isfield(M_, 'var') && isfield(M_.var, auxiliary_model_name)
auxiliary_model_type = 'var';
elseif isfield(M_, 'trend_component') && isfield(M_.trend_component, auxiliary_model_name)
auxiliary_model_type = 'trend_component';
else
error('Unknown type of auxiliary model.')
end
end
if nargout
A0 = [];
AR = [];
B = [];
end
get_ar_ec_matrices(auxiliary_model_name, auxiliary_model_type);
% Get the number of lags
p = size(oo_.(auxiliary_model_type).(auxiliary_model_name).ar, 3);
% Get the number of variables
n = length(oo_.(auxiliary_model_type).(auxiliary_model_name).ar(:,:,1));
switch auxiliary_model_type
case 'var'
oo_.var.(auxiliary_model_name).CompanionMatrix = zeros(n*p);
oo_.var.(auxiliary_model_name).CompanionMatrix(1:n,1:n) = oo_.var.(auxiliary_model_name).ar(:,:,1);
for i=2:p
oo_.var.(auxiliary_model_name).CompanionMatrix(1:n,(i-1)*n+(1:n)) = oo_.var.(auxiliary_model_name).ar(:,:,i);
oo_.var.(auxiliary_model_name).CompanionMatrix((i-1)*n+(1:n),(i-2)*n+(1:n)) = eye(n);
end
AR = oo_.var.(auxiliary_model_name).ar;
M_.var.(auxiliary_model_name).list_of_variables_in_companion_var = M_.endo_names(M_.var.(auxiliary_model_name).lhs);
case 'trend_component'
% Get number of trends.
q = sum(M_.trend_component.(auxiliary_model_name).targets);
% Get the number of equations with error correction.
m = n-q;
% Get the indices of trend and EC equations in the auxiliary model.
target_eqnums_in_auxiliary_model = find(M_.trend_component.(auxiliary_model_name).targets);
ecm_eqnums_in_auxiliary_model = find(~M_.trend_component.(auxiliary_model_name).targets);
% REMARK It is assumed that the non trend equations are the error correction
% equations. We assume that the model can be cast in the following form:
%
% Δ Xₜ₋₁ = A₀ (Xₜ₋₁ - Zₜ₋₁) + Σᵢ₌₁ᵖ Aᵢ Δ Xₜ₋ᵢ + ϵₜ
%
% Zₜ = Zₜ₋₁ + ηₜ
%
% We first recast the equation into this representation, and
% we rewrite the model in levels (we integrate the first set
% of equations) to rewrite the model as a VAR(1) model. Let
% Yₜ = [Xₜ; Zₜ] be the vertical concatenation of vectors
% Xₜ (variables with EC) and Zₜ (trends). We have
%
% Yₜ = Σᵢ₌₁ᵖ⁺¹ Bᵢ Yₜ₋ᵢ + [εₜ; ηₜ]
%
% with
%
% B₁ = [I+Λ+A₁, -Λ; 0, I]
%
% Bᵢ = [Aᵢ-Aᵢ₋₁, 0; 0, 0] for i = 2,…, p
% and
% Bₚ₊₁ = -[Aₚ, 0; 0, 0]
%
% where the dimensions of I and 0 matrices can easily be
% deduced from the number of EC and trend equations.
% Check that the lhs of candidate ecm equations are at least first differences.
for i=1:m
if ~get_difference_order(M_.trend_component.(auxiliary_model_name).lhs(ecm_eqnums_in_auxiliary_model(i)))
error('Model %s is not a Trend component model! LHS variables should be in difference', auxiliary_model_name)
end
end
% Reorder target_eqnums_in_auxiliary_model to ensure that the order of
% the trend variables matches the order of the error correction
% variables.
[~,reorder] = ismember(M_.trend_component.(auxiliary_model_name).lhs(target_eqnums_in_auxiliary_model), ...
M_.trend_component.(auxiliary_model_name).target_vars(find(M_.trend_component.(auxiliary_model_name).target_vars>0)));
target_eqnums_in_auxiliary_model = target_eqnums_in_auxiliary_model(reorder);
% Get the EC matrix (the EC term is assumend to be in t-1).
%
% TODO: Check that the EC term is the difference between the
% endogenous variable and the trend variable.
%
A0 = oo_.trend_component.(auxiliary_model_name).ec(ecm_eqnums_in_auxiliary_model,:,1);
% Get the AR matrices.
AR = oo_.trend_component.(auxiliary_model_name).ar(ecm_eqnums_in_auxiliary_model,ecm_eqnums_in_auxiliary_model,:);
% Build B matrices (VAR in levels)
B(ecm_eqnums_in_auxiliary_model,ecm_eqnums_in_auxiliary_model,1) = eye(m)+A0+AR(:,:,1);
B(ecm_eqnums_in_auxiliary_model,target_eqnums_in_auxiliary_model) = -A0;
B(target_eqnums_in_auxiliary_model,target_eqnums_in_auxiliary_model) = eye(q);
for i=2:p
B(ecm_eqnums_in_auxiliary_model,ecm_eqnums_in_auxiliary_model,i) = AR(:,:,i)-AR(:,:,i-1);
end
B(ecm_eqnums_in_auxiliary_model,ecm_eqnums_in_auxiliary_model,p+1) = -AR(:,:,p);
% Write Companion matrix
oo_.trend_component.(auxiliary_model_name).CompanionMatrix = zeros(size(B, 1)*size(B, 3));
for i=1:p
oo_.trend_component.(auxiliary_model_name).CompanionMatrix(1:n, (i-1)*n+(1:n)) = B(:,:,i);
oo_.trend_component.(auxiliary_model_name).CompanionMatrix(i*n+(1:n),(i-1)*n+(1:n)) = eye(n);
end
oo_.trend_component.(auxiliary_model_name).CompanionMatrix(1:n, p*n+(1:n)) = B(:,:,p+1);
M_.trend_component.(auxiliary_model_name).list_of_variables_in_companion_var = M_.endo_names(M_.trend_component.(auxiliary_model_name).lhs);
variables_rewritten_in_levels = M_.trend_component.(auxiliary_model_name).list_of_variables_in_companion_var(ecm_eqnums_in_auxiliary_model);
for i=1:m
id = get_aux_variable_id(variables_rewritten_in_levels{i});
if id
auxinfo = M_.aux_vars(id);
if auxinfo.type==8
M_.trend_component.(auxiliary_model_name).list_of_variables_in_companion_var(ecm_eqnums_in_auxiliary_model(i)) = ...
{M_.endo_names{auxinfo.orig_index}};
else
error('This is a bug. Please contact the Dynare Team.')
end
else
error('This is a bug. Please contact the Dynare Team.')
end
end
end
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