127 lines
3.2 KiB
Matlab
127 lines
3.2 KiB
Matlab
|
% stephane.adjemian@ens.fr
|
||
|
function [omega,f] = UnivariateSpectralDensity(dr,var_list)
|
||
|
% This function computes the theoretical spectral density of each
|
||
|
% endogenous variable declared in var_list. Results are stored in
|
||
|
% oo_ and may be plotted.
|
||
|
%
|
||
|
% Adapted from th_autocovariances.m.
|
||
|
global options_ oo_ M_
|
||
|
|
||
|
omega = []; f = [];
|
||
|
|
||
|
if options_.order > 1
|
||
|
disp('UnivariateSpectralDensity :: I Cannot compute the theoretical spectral density')
|
||
|
disp('with a second order approximation of the DSGE model!')
|
||
|
disp('Set order = 1.')
|
||
|
return
|
||
|
end
|
||
|
|
||
|
pltinfo = 1;%options_.SpectralDensity.Th.plot;
|
||
|
cutoff = 100;%options_.SpectralDensity.Th.cutoff;
|
||
|
sdl = 0.1;%options_.SepctralDensity.Th.sdl;
|
||
|
omega = (0:sdl:pi)';
|
||
|
GridSize = length(omega);
|
||
|
exo_names_orig_ord = M_.exo_names_orig_ord;
|
||
|
if sscanf(version('-release'),'%d') < 13
|
||
|
warning off
|
||
|
else
|
||
|
eval('warning off MATLAB:dividebyzero')
|
||
|
end
|
||
|
if nargin<2
|
||
|
var_list = [];
|
||
|
end
|
||
|
nvar = size(var_list,1);
|
||
|
if nvar == 0
|
||
|
nvar = length(dr.order_var);
|
||
|
ivar = [1:nvar]';
|
||
|
else
|
||
|
ivar=zeros(nvar,1);
|
||
|
for i=1:nvar
|
||
|
i_tmp = strmatch(var_list(i,:),M_.endo_names,'exact');
|
||
|
if isempty(i_tmp)
|
||
|
error (['One of the variable specified does not exist']) ;
|
||
|
else
|
||
|
ivar(i) = i_tmp;
|
||
|
end
|
||
|
end
|
||
|
end
|
||
|
f = zeros(nvar,GridSize);
|
||
|
ghx = dr.ghx;
|
||
|
ghu = dr.ghu;
|
||
|
npred = dr.npred;
|
||
|
nstatic = dr.nstatic;
|
||
|
kstate = dr.kstate;
|
||
|
order = dr.order_var;
|
||
|
iv(order) = [1:length(order)];
|
||
|
nx = size(ghx,2);
|
||
|
ikx = [nstatic+1:nstatic+npred];
|
||
|
A = zeros(nx,nx);
|
||
|
k0 = kstate(find(kstate(:,2) <= M_.maximum_lag+1),:);
|
||
|
i0 = find(k0(:,2) == M_.maximum_lag+1);
|
||
|
i00 = i0;
|
||
|
n0 = length(i0);
|
||
|
A(i0,:) = ghx(ikx,:);
|
||
|
AS = ghx(:,i0);
|
||
|
ghu1 = zeros(nx,M_.exo_nbr);
|
||
|
ghu1(i0,:) = ghu(ikx,:);
|
||
|
for i=M_.maximum_lag:-1:2
|
||
|
i1 = find(k0(:,2) == i);
|
||
|
n1 = size(i1,1);
|
||
|
j1 = zeros(n1,1);
|
||
|
j2 = j1;
|
||
|
for k1 = 1:n1
|
||
|
j1(k1) = find(k0(i00,1)==k0(i1(k1),1));
|
||
|
j2(k1) = find(k0(i0,1)==k0(i1(k1),1));
|
||
|
end
|
||
|
AS(:,j1) = AS(:,j1)+ghx(:,i1);
|
||
|
i0 = i1;
|
||
|
end
|
||
|
b = ghu1*M_.Sigma_e*ghu1';
|
||
|
[A,B] = kalman_transition_matrix(dr);
|
||
|
% index of predetermined variables in A
|
||
|
i_pred = [nstatic+(1:npred) M_.endo_nbr+1:length(A)];
|
||
|
A = A(i_pred,i_pred);
|
||
|
[vx, ns_var] = lyapunov_symm(A,b);
|
||
|
i_ivar = find(~ismember(ivar,dr.order_var(ns_var+nstatic)));
|
||
|
ivar = ivar(i_ivar);
|
||
|
iky = iv(ivar);
|
||
|
aa = ghx(iky,:);
|
||
|
bb = ghu(iky,:);
|
||
|
Gamma = zeros(nvar,cutoff+1);
|
||
|
tmp = aa*vx*aa'+ bb*M_.Sigma_e*bb';
|
||
|
k = find(abs(tmp) < 1e-12);
|
||
|
tmp(k) = 0;
|
||
|
Gamma(:,1) = diag(tmp);
|
||
|
vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
|
||
|
tmp = aa*vxy;
|
||
|
k = find(abs(tmp) < 1e-12);
|
||
|
tmp(k) = 0;
|
||
|
Gamma(:,2) = diag(tmp);
|
||
|
for i=2:cutoff
|
||
|
vxy = A*vxy;
|
||
|
tmp = aa*vxy;
|
||
|
k = find(abs(tmp) < 1e-12);
|
||
|
tmp(k) = 0;
|
||
|
Gamma(:,i+1) = diag(tmp);
|
||
|
end
|
||
|
H = 1:cutoff;
|
||
|
for i=1:nvar
|
||
|
f(i,:) = Gamma(i,1)/(2*pi) + Gamma(i,H+1)*cos(H'*omega')/pi;
|
||
|
end
|
||
|
|
||
|
if sscanf(version('-release'),'%d') < 13
|
||
|
warning on
|
||
|
else
|
||
|
eval('warning on MATLAB:dividebyzero')
|
||
|
end
|
||
|
|
||
|
if pltinfo
|
||
|
for i= 1:nvar
|
||
|
figure('Name',['Spectral Density of ' deblank(M_.endo_names(ivar(i),:)) '.'])
|
||
|
plot(omega,f(i,:),'-k','linewidth',2)
|
||
|
xlabel('0 \leq \omega \leq \pi')
|
||
|
ylabel('f(\omega)')
|
||
|
box on
|
||
|
axis tight
|
||
|
end
|
||
|
end
|