103 lines
2.8 KiB
Matlab
103 lines
2.8 KiB
Matlab
function bvar_density(maxnlags)
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% function bvar_density(maxnlags)
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% computes the density of a bayesian var
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%
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% INPUTS
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% maxnlags: maximum number of lags in the bvar
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%
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% OUTPUTS
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% none
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright © 2003-2007 Christopher Sims
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% Copyright © 2007-2017 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_
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oo_.bvar.log_marginal_data_density=NaN(maxnlags,1);
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for nlags = 1:maxnlags
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[ny, nx, posterior, prior] = bvar_toolbox(nlags);
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oo_.bvar.posterior{nlags}=posterior;
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oo_.bvar.prior{nlags}=prior;
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posterior_int = matrictint(posterior.S, posterior.df, posterior.XXi);
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prior_int = matrictint(prior.S, prior.df, prior.XXi);
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lik_nobs = posterior.df - prior.df;
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log_dnsty = posterior_int - prior_int - 0.5*ny*lik_nobs*log(2*pi);
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oo_.bvar.log_marginal_data_density(nlags)=log_dnsty;
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skipline()
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fprintf('The marginal log density of the BVAR(%g) model is equal to %10.4f\n', ...
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nlags, log_dnsty);
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skipline()
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end
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function w = matrictint(S, df, XXi)
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% Computes the log of the integral of the kernel of the PDF of a
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% normal-inverse-Wishart distribution.
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%
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% S: parameter of inverse-Wishart distribution
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% df: number of degrees of freedom of inverse-Wishart distribution
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% XXi: first component of VCV matrix of matrix-normal distribution
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%
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% Computes the integral over (Phi, Sigma) of:
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%
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% det(Sigma)^(-k/2)*exp(-0.5*Tr((Phi-PhiHat)'*(XXi)^(-1)*(Phi-PhiHat)*Sigma^(-1)))*
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% det(Sigma)^((df+ny+1)/2)*exp(-0.5*Tr(Sigma^(-1)*S))
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%
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% (where k is the dimension of XXi and ny is the dimension of S and
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% Sigma)
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% Original file downloaded from:
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% http://sims.princeton.edu/yftp/VARtools/matlab/matrictint.m
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k=size(XXi,1);
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ny=size(S,1);
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[cx,p]=chol(XXi);
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[cs,q]=chol(S);
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if any(diag(cx)<100*eps)
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error('singular XXi')
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end
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if any(diag(cs<100*eps))
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error('singular S')
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end
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% Matrix-normal component
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w1 = 0.5*k*ny*log(2*pi)+ny*sum(log(diag(cx)));
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% Inverse-Wishart component
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w2 = -df*sum(log(diag(cs))) + 0.5*df*ny*log(2) + ny*(ny-1)*0.25*log(pi) + ggammaln(ny, df);
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w = w1 + w2;
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function lgg = ggammaln(m, df)
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if df <= (m-1)
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error('too few df in ggammaln')
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else
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garg = 0.5*(df+(0:-1:1-m));
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lgg = sum(gammaln(garg));
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end
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