162 lines
7.2 KiB
Matlab
162 lines
7.2 KiB
Matlab
function [A0, A0star, AR, B] = get_companion_matrix(auxiliary_model_name, auxiliary_model_type)
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% Gets the companion VAR representation of a PAC auxiliary model.
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% Depending on the nature of this auxiliary model the output is
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% saved in oo_.{var,trend_component}.(auxiliary_model_name).CompanionMatrix
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%
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% INPUTS
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% - auxiliary_model_name [string] the name of the auxiliary model
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% - auxiliary_model_type [string] the type of the auxiliary model
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% ('var' or 'trend_component')
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%
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% OUTPUTS
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% - None
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% Copyright © 2018-2019 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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global oo_ M_
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if nargin < 2
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if isfield(M_, 'var') && isfield(M_.var, auxiliary_model_name)
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auxiliary_model_type = 'var';
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elseif isfield(M_, 'trend_component') && isfield(M_.trend_component, auxiliary_model_name)
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auxiliary_model_type = 'trend_component';
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else
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error('Unknown type of auxiliary model.')
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end
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end
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if strcmp(auxiliary_model_type, 'var')
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[AR, ~, Constant] = feval(sprintf('%s.varmatrices', M_.fname), auxiliary_model_name, M_.params, M_.var.(auxiliary_model_name).structural);
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isconstant = any(abs(Constant)>0);
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M_.var.(auxiliary_model_name).isconstant = isconstant; % FIXME Could be done by preprocessor instead…
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elseif strcmp(auxiliary_model_type, 'trend_component')
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[AR, A0, A0star] = feval(sprintf('%s.trend_component_ar_a0', M_.fname), auxiliary_model_name, M_.params);
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else
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error('Unknown type of auxiliary model.')
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end
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% Get the number of lags
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p = size(AR, 3);
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% Get the number of variables
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n = length(M_.(auxiliary_model_type).(auxiliary_model_name).lhs);
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switch auxiliary_model_type
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case 'var'
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oo_.var.(auxiliary_model_name).CompanionMatrix = zeros(n*p+isconstant);
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oo_.var.(auxiliary_model_name).CompanionMatrix(isconstant+(1:n),isconstant+(1:n)) = AR(:,:,1);
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for i = 2:p
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oo_.var.(auxiliary_model_name).CompanionMatrix(isconstant+(1:n),isconstant+(i-1)*n+(1:n)) = AR(:,:,i);
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oo_.var.(auxiliary_model_name).CompanionMatrix(isconstant+(i-1)*n+(1:n),isconstant+(i-2)*n+(1:n)) = eye(n);
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end
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if isconstant
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oo_.var.(auxiliary_model_name).CompanionMatrix(1,1) = 1;
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for i=1:n
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oo_.var.(auxiliary_model_name).CompanionMatrix(1+i,1) = Constant(i);
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end
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end
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M_.var.(auxiliary_model_name).list_of_variables_in_companion_var = M_.endo_names(M_.var.(auxiliary_model_name).lhs);
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if nargout
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A0 = [];
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A0star = [];
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B = [];
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end
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case 'trend_component'
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% Get number of trends.
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q = sum(M_.trend_component.(auxiliary_model_name).targets);
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% Get the number of equations with error correction.
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m = n - q;
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% Get the indices of trend and EC equations in the auxiliary model.
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target_eqnums_in_auxiliary_model = M_.trend_component.(auxiliary_model_name).target_eqn;
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ecm_eqnums_in_auxiliary_model = find(~M_.trend_component.(auxiliary_model_name).targets);
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% REMARK It is assumed that the non trend equations are the error correction
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% equations. We assume that the model can be cast in the following form:
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%
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% Δ Xₜ₋₁ = A₀ (Xₜ₋₁ - C₀Zₜ₋₁) + Σᵢ₌₁ᵖ Aᵢ Δ Xₜ₋ᵢ + ϵₜ
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%
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% Zₜ = Zₜ₋₁ + ηₜ
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%
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% where Xₜ is a n×1 vector and Zₜ is an m×1 vector, A₀ is a
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% n×n matrix, C₀ a n×m matrix, and Aᵢ (i=1,…,p) are n×n
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% matrices. Matrix C₀ can be factorized as C₀ = (A₀)⁻¹×Λ,
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% where Λ is a n×m matrix.
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%
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% We rewrite the model in levels (we integrate the first set
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% of equations) and rewrite the model as a VAR(1) model. Let
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% Yₜ = [Xₜ; Zₜ] be the vertical concatenation of vectors
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% Xₜ (variables with EC) and Zₜ (trends). We have
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%
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% Yₜ = Σᵢ₌₁ᵖ⁺¹ Bᵢ Yₜ₋ᵢ + [εₜ; ηₜ]
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%
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% with
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%
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% B₁ = [I+A₀+A₁, -Λ; 0, I]
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%
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% Bᵢ = [Aᵢ-Aᵢ₋₁, 0; 0, 0] for i = 2,…, p
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% and
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% Bₚ₊₁ = -[Aₚ, 0; 0, 0]
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%
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% where the dimensions of I and 0 matrices can easily be
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% deduced from the number of EC and trend equations.
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% Check that the lhs of candidate ecm equations are at least first differences.
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for i = 1:m
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if ~get_difference_order(M_.trend_component.(auxiliary_model_name).lhs(ecm_eqnums_in_auxiliary_model(i)))
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error([auxiliary_model_name ' is not a trend component model. The LHS variables should be in differences'])
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end
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end
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% Get the EC matrix (the EC term is assumend to be in t-1).
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%
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% TODO: Check that the EC term is the difference between the
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% endogenous variable and the trend variable.
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%
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% Build B matrices (VAR in levels)
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B = zeros(m+q, m+q, p+1);
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B(ecm_eqnums_in_auxiliary_model, ecm_eqnums_in_auxiliary_model, 1) = eye(m) + A0 + AR(:,:,1);
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B(ecm_eqnums_in_auxiliary_model, target_eqnums_in_auxiliary_model) = -A0star;
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B(target_eqnums_in_auxiliary_model, target_eqnums_in_auxiliary_model) = eye(q);
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for i = 2:p
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B(ecm_eqnums_in_auxiliary_model,ecm_eqnums_in_auxiliary_model,i) = AR(:,:,i) - AR(:,:,i-1);
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end
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B(ecm_eqnums_in_auxiliary_model,ecm_eqnums_in_auxiliary_model,p+1) = -AR(:,:,p);
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% Write Companion matrix
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oo_.trend_component.(auxiliary_model_name).CompanionMatrix = zeros(size(B, 1)*size(B, 3));
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for i = 1:p
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oo_.trend_component.(auxiliary_model_name).CompanionMatrix(1:n, (i-1)*n+(1:n)) = B(:,:,i);
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oo_.trend_component.(auxiliary_model_name).CompanionMatrix(i*n+(1:n),(i-1)*n+(1:n)) = eye(n);
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end
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oo_.trend_component.(auxiliary_model_name).CompanionMatrix(1:n, p*n+(1:n)) = B(:,:,p+1);
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M_.trend_component.(auxiliary_model_name).list_of_variables_in_companion_var = M_.endo_names(M_.trend_component.(auxiliary_model_name).lhs);
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variables_rewritten_in_levels = M_.trend_component.(auxiliary_model_name).list_of_variables_in_companion_var(ecm_eqnums_in_auxiliary_model);
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for i=1:m
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id = get_aux_variable_id(variables_rewritten_in_levels{i});
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if id
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auxinfo = M_.aux_vars(id);
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if auxinfo.type==8
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M_.trend_component.(auxiliary_model_name).list_of_variables_in_companion_var(ecm_eqnums_in_auxiliary_model(i)) = ...
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{M_.endo_names{auxinfo.orig_index}};
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else
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error('This is a bug. Please contact the Dynare Team.')
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end
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else
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error('This is a bug. Please contact the Dynare Team.')
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end
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end
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end |