Added Stochastic Extended Path method (SEP).
Stéphane Adjemian (Charybdis)
parent
7ff36b680b
commit
744f3fd41b
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@ -79,7 +79,7 @@ make_ex_;
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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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time_series = zeros(M_.endo_nbr,sample_size);
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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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@ -106,18 +106,28 @@ if options_.ep.stochastic
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[r,w] = gauss_hermite_weights_and_nodes(options_.ep.number_of_nodes);
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switch options_.ep.stochastic
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case 1
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rr = cell(1);
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ww = cell(1);
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for i=1:size(M_.Sigma_e,1)
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rr = {r};
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ww = {w};
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if M_.exo_nbr>1
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rr = cell(1);
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ww = cell(1);
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for i=1:size(M_.Sigma_e,1)
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rr = {r};
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ww = {w};
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end
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rrr = cartesian_product_of_sets(rr{:});
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www = cartesian_product_of_sets(ww{:});
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else
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rrr = r;
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www = w;
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end
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rrr = cartesian_product_of_sets(rr{:});
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www = cartesian_product_of_sets(ww{:});
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www = prod(www,2);
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nnn = length(www);
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otherwise
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error(['Order ' int2str(options_.ep.stochastic) ' Stochastic Extended Path method is not implemented!'])
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end
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else
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rrr = zeros(1,number_of_structural_innovations);
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www = 1;
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nnn = 1;
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end
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% Initializes some variables.
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@ -158,140 +168,137 @@ while (t<sample_size)
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shocks = oo_.ep.shocks(t,:);
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% Put it in oo_.exo_simul (second line).
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oo_.exo_simul(2,positive_var_indx) = shocks;
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if options_.ep.init && t==1% Compute first order solution.
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initial_path = simult_(initial_conditions,oo_.dr,oo_.exo_simul(2:end,:),1);
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if options_.ep.init==1
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oo_.endo_simul(:,1:end-1) = initial_path(:,1:end-1);% Last column is the steady state.
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elseif options_.ep.init==2
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oo_.endo_simul(:,1:end-1) = initial_path(:,1:end-1)*lambda+oo_.endo_simul(:,1:end-1)*(1-lambda);
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end
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end
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% Solve a perfect foresight model (using bytecoded version).
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increase_periods = 0;
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endo_simul = oo_.endo_simul;
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while 1
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if ~increase_periods
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t0 = tic;
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[flag,tmp] = bytecode('dynamic');
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ctime = toc(t0);
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info.convergence = ~flag;
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info.time = ctime;
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end
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if verbosity
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if info.convergence
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if t<10
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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elseif t<100
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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else
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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end
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else
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if t<10
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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elseif t<100
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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else
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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end
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for s = 1:nnn
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oo_.exo_simul(3,positive_var_indx) = rrr(s,:)*covariance_matrix_upper_cholesky;
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if options_.ep.init && s==1% Compute first order solution. t==1 &&
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initial_path = simult_(initial_conditions,oo_.dr,oo_.exo_simul(2:end,:),1);
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if options_.ep.init==1
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oo_.endo_simul(:,1:end-1) = initial_path(:,1:end-1);% Last column is the steady state.
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elseif options_.ep.init==2
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oo_.endo_simul(:,1:end-1) = initial_path(:,1:end-1)*lambda+oo_.endo_simul(:,1:end-1)*(1-lambda);
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end
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end
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% Test if periods is big enough.
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if ~increase_periods && max(max(abs(tmp(idx,end-options_.ep.lp:end)./tmp(idx,end-options_.ep.lp-1:end-1)-1)))<options_.dynatol.x
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break
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else
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options_.periods = options_.periods + options_.ep.step;
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options_.minimal_solving_period = options_.periods;
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increase_periods = increase_periods + 1;
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if verbosity
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if t<10
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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elseif t<100
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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else
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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end
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end
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if info.convergence
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oo_.endo_simul = [ tmp , repmat(oo_.steady_state,1,options_.ep.step) ];
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oo_.exo_simul = [ oo_.exo_simul ; zeros(options_.ep.step,size(shocks,2)) ];
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tmp_old = tmp;
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else
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oo_.endo_simul = [ oo_.endo_simul , repmat(oo_.steady_state,1,options_.ep.step) ];
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oo_.exo_simul = [ oo_.exo_simul ; zeros(options_.ep.step,size(shocks,2)) ];
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end
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t0 = tic;
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[flag,tmp] = bytecode('dynamic');
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ctime = toc(t0);
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info.time = info.time+ctime;
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if info.convergence
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maxdiff = max(max(abs(tmp(:,2:options_.ep.fp)-tmp_old(:,2:options_.ep.fp))));
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if maxdiff<options_.dynatol.x
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options_.periods = options_.ep.periods;
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options_.minimal_solving_period = options_.periods;
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oo_.exo_simul = oo_.exo_simul(1:(options_.periods+2),:);
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break
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end
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else
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% Solve a perfect foresight model (using bytecoded version).
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increase_periods = 0;
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endo_simul = oo_.endo_simul;
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while 1
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if ~increase_periods
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t0 = tic;
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[flag,tmp] = bytecode('dynamic');
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ctime = toc(t0);
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info.convergence = ~flag;
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info.time = ctime;
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end
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if verbosity
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if info.convergence
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continue
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if t<10
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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elseif t<100
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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else
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disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
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end
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else
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if increase_periods==10;
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if verbosity
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if t<10
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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elseif t<100
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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else
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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end
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end
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if t<10
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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elseif t<100
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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else
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disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
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end
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end
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end
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% Test if periods is big enough.
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if ~increase_periods && max(max(abs(tmp(idx,end-options_.ep.lp:end)./tmp(idx,end-options_.ep.lp-1:end-1)-1)))<options_.dynatol.x
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break
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else
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options_.periods = options_.periods + options_.ep.step;
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options_.minimal_solving_period = options_.periods;
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increase_periods = increase_periods + 1;
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if verbosity
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if t<10
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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elseif t<100
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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else
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disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
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end
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end
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if info.convergence
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oo_.endo_simul = [ tmp , repmat(oo_.steady_state,1,options_.ep.step) ];
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oo_.exo_simul = [ oo_.exo_simul ; zeros(options_.ep.step,size(shocks,2)) ];
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tmp_old = tmp;
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else
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oo_.endo_simul = [ oo_.endo_simul , repmat(oo_.steady_state,1,options_.ep.step) ];
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oo_.exo_simul = [ oo_.exo_simul ; zeros(options_.ep.step,size(shocks,2)) ];
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end
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t0 = tic;
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[flag,tmp] = bytecode('dynamic');
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ctime = toc(t0);
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info.time = info.time+ctime;
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if info.convergence
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maxdiff = max(max(abs(tmp(:,2:options_.ep.fp)-tmp_old(:,2:options_.ep.fp))));
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if maxdiff<options_.dynatol.x
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options_.periods = options_.ep.periods;
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options_.minimal_solving_period = options_.periods;
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oo_.exo_simul = oo_.exo_simul(1:(options_.periods+2),:);
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break
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end
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else
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info.convergence = ~flag;
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if info.convergence
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continue
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else
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if increase_periods==10;
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if verbosity
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if t<10
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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elseif t<100
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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elseif t<1000
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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else
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disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
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end
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end
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break
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end
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end
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end
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end
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end
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end
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if ~info.convergence% If the previous step was unsuccesfull, use an homotopic approach
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[INFO,tmp] = homotopic_steps(.5,.01,t);
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% Cumulate time.
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info.time = ctime+INFO.time;
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if (~isstruct(INFO) && isnan(INFO)) || ~INFO.convergence
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disp('Homotopy:: No convergence of the perfect foresight model solver!')
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error('I am not able to simulate this model!');
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else
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info.convergence = 1;
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oo_.endo_simul = tmp;
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if verbosity && info.convergence
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disp('Homotopy:: Convergence of the perfect foresight model solver!')
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if ~info.convergence% If the previous step was unsuccesfull, use an homotopic approach
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[INFO,tmp] = homotopic_steps(.5,.01,t);
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% Cumulate time.
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info.time = ctime+INFO.time;
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if (~isstruct(INFO) && isnan(INFO)) || ~INFO.convergence
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disp('Homotopy:: No convergence of the perfect foresight model solver!')
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error('I am not able to simulate this model!');
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else
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info.convergence = 1;
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oo_.endo_simul = tmp;
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if verbosity && info.convergence
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disp('Homotopy:: Convergence of the perfect foresight model solver!')
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end
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end
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else
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oo_.endo_simul = tmp;
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end
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else
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oo_.endo_simul = tmp;
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% Save results of the perfect foresight model solver.
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time_series(:,t) = time_series(:,t)+ www(s)*oo_.endo_simul(:,2);
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%save('simulated_paths.mat','time_series');
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% Set initial condition for the nex round.
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%initial_conditions = oo_.endo_simul(:,2);
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end
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if nargin==6
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zlb_periods = find(oo_.endo_simul(zlb_idx,:)<=1+1e-12);
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zlb_number_of_periods = length(zlb_periods);
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if zlb_number_of_periods
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count_zlb = [count_zlb ; [t, zlb_number_of_periods, zlb_periods(1) , zlb_periods(end)] ];
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end
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end
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% Save results of the perfect foresight model solver.
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time_series(:,t) = oo_.endo_simul(:,2);
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save('simulated_paths.mat','time_series');
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% Set initial condition for the nex round.
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%initial_conditions = oo_.endo_simul(:,2);
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oo_.endo_simul = oo_.endo_simul(:,1:options_.periods+2);
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oo_.endo_simul(:,1:end-1) = oo_.endo_simul(:,2:end);
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%oo_.endo_simul = oo_.endo_simul(:,1:options_.periods+M_.maximum_endo_lag+M_.maximum_endo_lead);
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oo_.endo_simul(:,1:end-1) = oo_.endo_simul(:,2:end);
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oo_.endo_simul(:,1) = time_series(:,t);
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oo_.endo_simul(:,end) = oo_.steady_state;
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end
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@ -301,4 +308,6 @@ else
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if ~exist('OCTAVE_VERSION')
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fprintf(back);
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end
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end
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end
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oo_.endo_simul = oo_.steady_state;
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