136 lines
4.3 KiB
Matlab
136 lines
4.3 KiB
Matlab
function time_series = extended_path(initial_conditions,sample_size,init)
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% Stochastic simulation of a non linear DSGE model using the Extended Path method (Fair and Taylor 1983). A time
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% series of size T is obtained by solving T perfect foresight models.
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%
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% INPUTS
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% o initial_conditions [double] m*nlags array, where m is the number of endogenous variables in the model and
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% nlags is the maximum number of lags.
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% o sample_size [integer] scalar, size of the sample to be simulated.
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%
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% OUTPUTS
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% o time_series [double] m*sample_size array, the simulations.
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%
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% ALGORITHM
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%
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% SPECIAL REQUIREMENTS
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% Copyright (C) 2009 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 <http://www.gnu.org/licenses/>.
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global M_ oo_ options_
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% Set default initial conditions.
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if isempty(initial_conditions)
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initial_conditions = repmat(oo_.steady_state,1,M_.maximum_lag);
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end
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% Copy sample_size to periods.
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options_.periods = sample_size;
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% Initialize the exogenous variables.
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make_ex_;
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% Initialize the endogenous variables.
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make_y_;
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% Initialize the output array.
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time_series = NaN(M_.endo_nbr,sample_size+1);
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% Set the covariance matrix of the structural innovations.
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variances = diag(M_.Sigma_e);
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positive_var_indx = find(variances>0);
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covariance_matrix = M_.Sigma_e(positive_var_indx,positive_var_indx);
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number_of_structural_innovations = length(covariance_matrix);
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covariance_matrix_upper_cholesky = chol(covariance_matrix);
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tdx = M_.maximum_lag+1;
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norme = 0;
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% Set verbose option
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verbose = 0;
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for t=1:sample_size
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shocks = exp(randn(1,number_of_structural_innovations)*covariance_matrix_upper_cholesky-.5*variances(positive_var_indx)');
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oo_.exo_simul(tdx,positive_var_indx) = shocks;
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info = perfect_foresight_simulation;
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time = info.time;
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if verbose
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t
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info
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end
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if ~info.convergence
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info = homotopic_steps(tdx,positive_var_indx,shocks,norme,.2);
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if verbose
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norme
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info
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end
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else
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norme = sqrt(sum((shocks-1).^2,2));
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end
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if ~info.convergence
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error('I am not able to simulate this model!')
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end
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info.time = info.time+time;
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time_series(:,t+1) = oo_.endo_simul(:,tdx);
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oo_.endo_simul(:,1:end-1) = oo_.endo_simul(:,2:end);
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oo_.endo_simul(:,end) = oo_.steady_state;
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end
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function info = homotopic_steps(tdx,positive_var_indx,shocks,init_weight,step)
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global oo_
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weight = init_weight;
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verbose = 0;
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iter = 0;
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time = 0;
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reduce_step = 0;
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while iter<=100 && weight<=1
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iter = iter+1;
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old_weight = weight;
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weight = weight+step;
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oo_.exo_simul(tdx,positive_var_indx) = weight*shocks+(1-weight);
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info = perfect_foresight_simulation;
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time = time+info.time;
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if verbose
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[iter,step]
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[info.iterations.time,info.iterations.error]
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end
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if ~info.convergence
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if verbose
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disp('Reduce step size!')
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end
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reduce_step = 1;
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break
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else
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if length(info.iterations.error)<5
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if verbose
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disp('Increase step size!')
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end
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step = step*1.5;
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end
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end
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end
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if reduce_step
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step=step/1.5;
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info = homotopic_steps(tdx,positive_var_indx,shocks,old_weight,step);
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time = time+info.time;
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elseif weight<1 && iter<100
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oo_.exo_simul(tdx,positive_var_indx) = shocks;
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info = perfect_foresight_simulation;
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info.time = info.time+time;
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else
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info.time = time;
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end |