Fix UnivariateSpectralDensity.m for filtered variables
- Adds bandpass filter - Writes results to oo_time-shift
Johannes Pfeifer
parent
25df325899
commit
a4b04ca9b4
|
|
@ -1,11 +1,25 @@
|
|||
function [omega,f] = UnivariateSpectralDensity(dr,var_list)
|
||||
function [oo_] = UnivariateSpectralDensity(M_,oo_,options_,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. Plots are saved into the graphs-folder.
|
||||
% oo_.SpectralDensity and may be plotted. Plots are saved into the
|
||||
% graphs-folder.
|
||||
%
|
||||
% INPUTS
|
||||
% M_ [structure] Dynare's model structure
|
||||
% oo_ [structure] Dynare's results structure
|
||||
% options_ [structure] Dynare's options structure
|
||||
% var_list [integer] Vector of indices for a subset of variables.
|
||||
%
|
||||
% OUTPUTS
|
||||
% oo_ [structure] Dynare's results structure,
|
||||
% containing the subfield
|
||||
% SpectralDensity with fields freqs
|
||||
% and density, which are of size nvar*ngrid.
|
||||
%
|
||||
|
||||
% Adapted from th_autocovariances.m.
|
||||
|
||||
% Copyright (C) 2006-2013 Dynare Team
|
||||
% Copyright (C) 2006-2015 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
|
|
@ -22,10 +36,6 @@ function [omega,f] = UnivariateSpectralDensity(dr,var_list)
|
|||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
global options_ oo_ M_
|
||||
|
||||
|
||||
omega = []; f = [];
|
||||
|
||||
if options_.order > 1
|
||||
disp('UnivariateSpectralDensity :: I Cannot compute the theoretical spectral density')
|
||||
|
|
@ -33,12 +43,7 @@ if options_.order > 1
|
|||
disp('Please set order = 1. I abort')
|
||||
return
|
||||
end
|
||||
pltinfo = options_.SpectralDensity.plot;
|
||||
cutoff = options_.SpectralDensity.cutoff;
|
||||
sdl = options_.SpectralDensity.sdl;
|
||||
omega = (0:sdl:pi)';
|
||||
GridSize = length(omega);
|
||||
exo_names_orig_ord = M_.exo_names_orig_ord;
|
||||
|
||||
if isoctave
|
||||
warning('off', 'Octave:divide-by-zero')
|
||||
else
|
||||
|
|
@ -60,22 +65,19 @@ for i=1:nvar
|
|||
ivar(i) = i_tmp;
|
||||
end
|
||||
end
|
||||
f = zeros(nvar,GridSize);
|
||||
ghx = dr.ghx;
|
||||
ghu = dr.ghu;
|
||||
|
||||
ghx = oo_.dr.ghx;
|
||||
ghu = oo_.dr.ghu;
|
||||
nspred = M_.nspred;
|
||||
nstatic = M_.nstatic;
|
||||
kstate = dr.kstate;
|
||||
order = dr.order_var;
|
||||
kstate = oo_.dr.kstate;
|
||||
order = oo_.dr.order_var;
|
||||
iv(order) = [1:length(order)];
|
||||
nx = size(ghx,2);
|
||||
ikx = [nstatic+1:nstatic+nspred];
|
||||
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,:);
|
||||
|
|
@ -91,87 +93,72 @@ for i=M_.maximum_lag:-1:2
|
|||
AS(:,j1) = AS(:,j1)+ghx(:,i1);
|
||||
i0 = i1;
|
||||
end
|
||||
Gamma = zeros(nvar,cutoff+1);
|
||||
[A,B] = kalman_transition_matrix(dr,ikx',1:nx,M_.exo_nbr);
|
||||
|
||||
[A,B] = kalman_transition_matrix(oo_.dr,ikx',1:nx,M_.exo_nbr);
|
||||
[vx, u] = lyapunov_symm(A,B*M_.Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,[],[],options_.debug);
|
||||
iky = iv(ivar);
|
||||
if ~isempty(u)
|
||||
iky = iky(find(any(abs(ghx(iky,:)*u) < options_.Schur_vec_tol,2)));
|
||||
ivar = dr.order_var(iky);
|
||||
ivar = oo_.dr.order_var(iky);
|
||||
end
|
||||
|
||||
iky = iv(ivar);
|
||||
aa = ghx(iky,:);
|
||||
bb = ghu(iky,:);
|
||||
|
||||
if options_.hp_filter == 0
|
||||
tmp = aa*vx*aa'+ bb*M_.Sigma_e*bb';
|
||||
tmp(abs(tmp) < 1e-12) = 0;
|
||||
Gamma(:,1) = diag(tmp);
|
||||
vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
|
||||
tmp = aa*vxy;
|
||||
tmp(abs(tmp) < 1e-12) = 0;
|
||||
Gamma(:,2) = diag(tmp);
|
||||
for i=2:cutoff
|
||||
vxy = A*vxy;
|
||||
tmp = aa*vxy;
|
||||
tmp(abs(tmp) < 1e-12) = 0;
|
||||
Gamma(:,i+1) = diag(tmp);
|
||||
end
|
||||
else
|
||||
iky = iv(ivar);
|
||||
aa = ghx(iky,:);
|
||||
bb = ghu(iky,:);
|
||||
ngrid = options_.hp_ngrid; %number of grid points
|
||||
freqs = (0 : pi/(ngrid-1):pi)'; % grid on which to compute
|
||||
tpos = exp( sqrt(-1)*freqs); %positive frequencies
|
||||
tneg = exp(-sqrt(-1)*freqs); %negative frequencies
|
||||
if options_.hp_filter == 0 && ~options_.bandpass.indicator %do not filter
|
||||
filter_gain=ones(ngrid,1);
|
||||
elseif ~(options_.hp_filter == 0 && ~options_.bandpass.indicator) && options_.bandpass.indicator %filter with bandpass
|
||||
filter_gain = zeros(1,ngrid);
|
||||
lowest_periodicity=options_.bandpass.passband(2);
|
||||
highest_periodicity=options_.bandpass.passband(1);
|
||||
highest_periodicity=max(2,highest_periodicity); % restrict to upper bound of pi
|
||||
filter_gain(freqs>=2*pi/lowest_periodicity & freqs<=2*pi/highest_periodicity)=1;
|
||||
filter_gain(freqs<=-2*pi/lowest_periodicity+2*pi & freqs>=-2*pi/highest_periodicity+2*pi)=1;
|
||||
elseif ~(options_.hp_filter == 0 && ~options_.bandpass.indicator) && ~options_.bandpass.indicator %filter with HP-filter
|
||||
lambda = options_.hp_filter;
|
||||
ngrid = options_.hp_ngrid;
|
||||
freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));
|
||||
tpos = exp( sqrt(-1)*freqs);
|
||||
tneg = exp(-sqrt(-1)*freqs);
|
||||
hp1 = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
|
||||
mathp_col = NaN(ngrid,length(ivar)^2);
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [(IA-A*tneg(ig))\ghu1;IE]...
|
||||
*M_.Sigma_e*[ghu1'/(IA-A'*tpos(ig)) IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
|
||||
f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col(ig,:) = (f_hp(:))'; % store as matrix row
|
||||
% for ifft
|
||||
end;
|
||||
imathp_col = real(ifft(mathp_col))*(2*pi);
|
||||
tmp = reshape(imathp_col(1,:),nvar,nvar);
|
||||
tmp(abs(tmp)<1e-12) = 0;
|
||||
Gamma(:,1) = diag(tmp);
|
||||
sy = sqrt(Gamma(:,1));
|
||||
sy = sy *sy';
|
||||
for i=1:cutoff-1
|
||||
tmp = reshape(imathp_col(i+1,:),nvar,nvar)./sy;
|
||||
tmp(abs(tmp) < 1e-12) = 0;
|
||||
Gamma(:,i+1) = diag(tmp);
|
||||
end
|
||||
filter_gain = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
|
||||
end
|
||||
|
||||
H = 1:cutoff;
|
||||
mathp_col = NaN(ngrid,length(ivar)^2);
|
||||
IA = eye(size(A,1));
|
||||
IE = eye(M_.exo_nbr);
|
||||
for ig = 1:ngrid
|
||||
f_omega =(1/(2*pi))*( [(IA-A*tneg(ig))\ghu1;IE]...
|
||||
*M_.Sigma_e*[ghu1'/(IA-A'*tpos(ig)) IE]); % state variables
|
||||
g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
|
||||
f_hp = filter_gain(ig)^2*g_omega; % spectral density of selected filtered series
|
||||
mathp_col(ig,:) = (f_hp(:))'; % store as matrix row
|
||||
end;
|
||||
|
||||
f = zeros(nvar,ngrid);
|
||||
for i=1:nvar
|
||||
f(i,:) = Gamma(i,1)/(2*pi) + Gamma(i,H+1)*cos(H'*omega')/pi;
|
||||
f(i,:) = real(mathp_col(:,(i-1)*nvar+i)); %read out spectral density
|
||||
end
|
||||
|
||||
oo_.SpectralDensity.freqs=freqs;
|
||||
oo_.SpectralDensity.density=f;
|
||||
|
||||
if isoctave
|
||||
warning('on', 'Octave:divide-by-zero')
|
||||
else
|
||||
warning on MATLAB:dividebyzero
|
||||
end
|
||||
|
||||
if pltinfo
|
||||
if options_.nograph == 0
|
||||
if ~exist(M_.fname, 'dir')
|
||||
mkdir('.',M_.fname);
|
||||
end
|
||||
if ~exist([M_.fname '/graphs'])
|
||||
if ~exist([M_.fname '/graphs'],'dir')
|
||||
mkdir(M_.fname,'graphs');
|
||||
end
|
||||
|
||||
for i= 1:nvar
|
||||
hh = dyn_figure(options_,'Name',['Spectral Density of ' deblank(M_.endo_names(ivar(i),:)) '.']);
|
||||
plot(omega,f(i,:),'-k','linewidth',2)
|
||||
plot(freqs,f(i,:),'-k','linewidth',2)
|
||||
xlabel('0 \leq \omega \leq \pi')
|
||||
ylabel('f(\omega)')
|
||||
box on
|
||||
|
|
|
|||
|
|
@ -350,7 +350,7 @@ if options_.irf
|
|||
end
|
||||
|
||||
if options_.SpectralDensity.trigger == 1
|
||||
[omega,f] = UnivariateSpectralDensity(oo_.dr,var_list);
|
||||
[oo_] = UnivariateSpectralDensity(M_,oo_,options_,var_list);
|
||||
end
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue