dynare/matlab/DsgeVarLikelihood.m

function [fval,cost_flag,ys,trend_coeff,info,PHI,SIGMAu,iXX] = DsgeVarLikelihood(xparam1,gend)
% stephane.adjemian@ens.fr
global bayestopt_ estim_params_ M_ options_

nvx = estim_params_.nvx;
nvn = estim_params_.nvn;
ncx = estim_params_.ncx;
ncn = estim_params_.ncn;
np  = estim_params_.np;
nx = nvx+nvn+ncx+ncn+np;
ns = nvx+nvn+ncx+ncn;

NumberOfObservedVariables = size(options_.varobs,1);
NumberOfLags = options_.varlag;
NumberOfParameters = NumberOfObservedVariables*NumberOfLags ;

mYY = evalin('base', 'mYY');
mYX = evalin('base', 'mYX');
mXY = evalin('base', 'mXY');
mXX = evalin('base', 'mXX');

fval = [];
cost_flag = [];
ys = [];
trend_coeff = [];
xparam1_test = xparam1;
cost_flag  = 1;

if options_.mode_compute ~= 1 & any(xparam1 < bayestopt_.lb)
    k = find(xparam1 < bayestopt_.lb);
    fval = bayestopt_.penalty*min(1e3,exp(sum(bayestopt_.lb(k)-xparam1(k))));
    info = 41;
    cost_flag = 0;
    return;
end

if options_.mode_compute ~= 1 & any(xparam1 > bayestopt_.ub)
    k = find(xparam1 > bayestopt_.ub);
    fval = bayestopt_.penalty*min(1e3,exp(sum(xparam1(k)- bayestopt_.ub(k))));
    info = 42;
    cost_flag = 0;
    return;
end

Q = M_.Sigma_e;
for i=1:estim_params_.nvx
    k = estim_params_.var_exo(i,1);
    Q(k,k) = xparam1(i)*xparam1(i);
end
offset = estim_params_.nvx;
if estim_params_.nvn
    disp('DsgeVarLikelihood :: Measurement errors are not implemented!')
    return
end 
if estim_params_.ncx
    disp('DsgeVarLikelihood :: Correlated structural innovations are not yet implemented!')
    return
end

M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
M_.Sigma_e = Q;

%% Weight of the dsge prior:
dsge_prior_weight = M_.params(strmatch('dsge_prior_weight',M_.param_names));
if dsge_prior_weight<(NumberOfParameters+NumberOfObservedVariables)/gend;
    fval = bayestopt_.penalty*min(1e3,(NumberOfParameters+NumberOfObservedVariables)/gend-dsge_prior_weight);
    info = 51
    cost_flag = 0;
    return;
end

%------------------------------------------------------------------------------
% 2. call model setup & reduction program
%------------------------------------------------------------------------------
[T,R,SteadyState,info] = dynare_resolve(bayestopt_.restrict_var_list,...
                                        bayestopt_.restrict_columns,...
                                        bayestopt_.restrict_aux);
if info(1) == 1 | info(1) == 2 | info(1) == 5
    fval = bayestopt_.penalty;
    cost_flag = 0;
    return
elseif info(1) == 3 | info(1) == 4 | info(1) == 20
    fval = bayestopt_.penalty*min(1e3,exp(info(2)));
    cost_flag = 0;
    return
end
if options_.loglinear == 1
    constant = log(SteadyState(bayestopt_.mfys));
else
    constant = SteadyState(bayestopt_.mfys);
end
if bayestopt_.with_trend == 1
    disp('DsgeVarLikelihood :: Linear trend is not yet implemented!')
    return
end

%------------------------------------------------------------------------------
% 3. theorretical moments (second order)
%------------------------------------------------------------------------------
tmp = lyapunov_symm(T,R*Q*R');% I compute the variance-covariance matrix
                              % of the restricted state vector.
bayestopt_.mf = bayestopt_.mf1;
mf  = bayestopt_.mf1;


TheoreticalAutoCovarianceOfTheObservedVariables = ...
    zeros(NumberOfObservedVariables,NumberOfObservedVariables,NumberOfLags+1);
TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) = tmp(mf,mf);
for lag = 1:NumberOfLags
  tmp = T*tmp;
  TheoreticalAutoCovarianceOfTheObservedVariables(:,:,lag+1) = tmp(mf,mf);
end
GYX = zeros(NumberOfObservedVariables,NumberOfParameters);
for i=1:NumberOfLags
  GYX(:,(i-1)*NumberOfObservedVariables+1:i*NumberOfObservedVariables) = ...
      TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1);
end
GXX = kron(eye(NumberOfLags), ...
           TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1));
for i = 1:NumberOfLags-1
  tmp1 = diag(ones(NumberOfLags-i,1),i); 
  tmp2 = diag(ones(NumberOfLags-i,1),-i);
  GXX = GXX + kron(tmp1,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1));
  GXX = GXX + kron(tmp2,TheoreticalAutoCovarianceOfTheObservedVariables(:,:,i+1)');
end

GYY = TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1);

assignin('base','GYY',GYY);
assignin('base','GXX',GXX);
assignin('base','GYX',GYX);

if ~isinf(dsge_prior_weight) 
  SIGMAu = dsge_prior_weight*gend*TheoreticalAutoCovarianceOfTheObservedVariables(:,:,1) + mYY ;
  tmp1 = dsge_prior_weight*gend*GYX + mYX;
  tmp2 = inv(dsge_prior_weight*gend*GXX+mXX);
  SIGMAu = SIGMAu - tmp1*tmp2*tmp1';
  if ~ispd(SIGMAu)
      v = diag(SIGMAu);
      k = find(v<0);
      fval = bayestopt_.penalty*min(1e3,exp(abs(v(k))));
      info = 52;
      cost_flag = 0;
    return;      
  end
  SIGMAu = SIGMAu / (gend*(dsge_prior_weight+1));
  PHI = tmp2*tmp1';
  prodlng1 = sum(gammaln(.5*((1+dsge_prior_weight)*gend- ...
			     NumberOfObservedVariables*NumberOfLags ...
			     +1-(1:NumberOfObservedVariables)')));
  prodlng2 = sum(gammaln(.5*(dsge_prior_weight*gend- ...
			     NumberOfObservedVariables*NumberOfLags ...
			     +1-(1:NumberOfObservedVariables)')));  
  lik = .5*NumberOfObservedVariables*log(det(dsge_prior_weight*gend*GXX+mXX)) ...
	+ .5*((dsge_prior_weight+1)*gend-NumberOfParameters)*log(det((dsge_prior_weight+1)*gend*SIGMAu)) ...
	- .5*NumberOfObservedVariables*log(det(dsge_prior_weight*gend*GXX)) ...
	- .5*(dsge_prior_weight*gend-NumberOfParameters)*log(det(dsge_prior_weight*gend*(GYY-GYX*inv(GXX)*GYX'))) ...
	+ .5*NumberOfObservedVariables*gend*log(2*pi)  ...
	- .5*log(2)*NumberOfObservedVariables*((dsge_prior_weight+1)*gend-NumberOfParameters) ...
	+ .5*log(2)*NumberOfObservedVariables*(dsge_prior_weight*gend-NumberOfParameters) ...
	- prodlng1 + prodlng2;
else % cod<6F> par SM (s<>rement pas exact... Que font ici les moments empiriques ?).    
  tmp1 = GYX;
  tmp2 = inv(GXX);
  PHI  = tmp2*tmp1';
  SIGMAu = GYY - tmp1*tmp2*tmp1;
  % <20> finir de corriger...
  lik  = -.5*sum(diag(inv(tmp2)*(mYY-2*tmp1'*mYX'+tmp1'*mXX*tmp1))) ...
	-(gend/2)*log(det(tmp2));
end      

lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p1,bayestopt_.p2,bayestopt_.p3,bayestopt_.p4);
fval = (lik-lnprior);
iXX = tmp2;