196 lines
6.0 KiB
Matlab
196 lines
6.0 KiB
Matlab
% Copyright (C) 2001 Michel Juillard
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%
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% computes the theoretical auto-covariances, gamma_y, for an AR(p) process
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% with coefficients dr.ghx and dr.ghu and shock variances M_.Sigma_e
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% for a subset of variables ivar (indices in M_.endo_names)
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% Theoretical HP filtering is available as an option
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function gamma_y=th_autocovariances(dr,ivar)
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global M_ options_
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if sscanf(version('-release'),'%d') < 13
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warning off
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else
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eval('warning off MATLAB:dividebyzero')
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end
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nar = options_.ar;
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gamma_y = cell(nar+1,1);
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nvar = size(ivar,1);
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ghx = dr.ghx;
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ghu = dr.ghu;
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npred = dr.npred;
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nstatic = dr.nstatic;
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kstate = dr.kstate;
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order = dr.order_var;
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iv(order) = [1:length(order)];
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nx = size(ghx,2);
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ikx = [nstatic+1:nstatic+npred];
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A = zeros(nx,nx);
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k0 = kstate(find(kstate(:,2) <= M_.maximum_lag+1),:);
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i0 = find(k0(:,2) == M_.maximum_lag+1);
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n0 = length(i0);
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A(i0,:) = ghx(ikx,:);
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AS = ghx(:,i0);
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ghu1 = zeros(nx,M_.exo_nbr);
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ghu1(i0,:) = ghu(ikx,:);
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for i=M_.maximum_lag:-1:2
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i1 = find(k0(:,2) == i);
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n1 = size(i1,1);
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j1 = zeros(n1,1);
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j2 = j1;
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for k1 = 1:n1
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j1(k1) = find(k0(1:n0,1)==k0(i1(k1),1));
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j2(k1) = find(k0(i0,1)==k0(i1(k1),1));
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end
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A(i1,i0(j2))=eye(n1);
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AS(:,j1) = AS(:,j1)+ghx(:,i1);
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i0 = i1;
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end
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b = ghu1*M_.Sigma_e*ghu1';
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% order of variables with preset variances in ghx and ghu
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iky = iv(ivar);
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aa = ghx(iky,:);
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bb = ghu(iky,:);
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if options_.order == 2
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%save temp A AS b dr M_.Sigma_e ikx iky nx n0
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vx = lyapunov_symm(A,b);
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Ex = (dr.ghs2(ikx)+dr.ghxx(ikx,:)*vx(:)+dr.ghuu(ikx,:)*M_.Sigma_e(:))/2;
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Ex = (eye(n0)-AS(ikx,:))\Ex;
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gamma_y{nar+3} = AS(iky,:)*Ex+(dr.ghs2(iky)+dr.ghxx(iky,:)*vx(:)+dr.ghuu(iky,:)*M_.Sigma_e(:))/2;
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end
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if options_.hp_filter == 0
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if options_.order < 2
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vx = lyapunov_symm(A,b);
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end
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gamma_y{1} = aa*vx*aa'+ bb*M_.Sigma_e*bb';
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k = find(abs(gamma_y{1}) < 1e-12);
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gamma_y{1}(k) = 0;
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% autocorrelations
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if nar > 0
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vxy = (A*vx*aa'+ghu1*M_.Sigma_e*bb');
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sy = sqrt(diag(gamma_y{1}));
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sy = sy *sy';
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gamma_y{2} = aa*vxy./sy;
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for i=2:nar
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vxy = A*vxy;
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gamma_y{i+1} = aa*vxy./sy;
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end
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end
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% variance decomposition
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if M_.exo_nbr > 1
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gamma_y{nar+2} = zeros(nvar,M_.exo_nbr);
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SS(M_.exo_names_orig_ord,M_.exo_names_orig_ord)=M_.Sigma_e+1e-14*eye(M_.exo_nbr);
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cs = chol(SS)';
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b1(:,M_.exo_names_orig_ord) = ghu1;
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b1 = b1*cs;
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b2(:,M_.exo_names_orig_ord) = ghu(iky,:);
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b2 = b2*cs;
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vx = lyapunov_symm(A,b1*b1');
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vv = diag(aa*vx*aa'+b2*b2');
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for i=1:M_.exo_nbr
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vx1 = lyapunov_symm(A,b1(:,i)*b1(:,i)');
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gamma_y{nar+2}(:,i) = abs(diag(aa*vx1*aa'+b2(:,i)*b2(:,i)'))./vv;
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end
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end
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else
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lambda = options_.hp_filter;
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ngrid = options_.hp_ngrid;
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freqs = 0 : ((2*pi)/ngrid) : (2*pi*(1 - .5/ngrid));
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tpos = exp( sqrt(-1)*freqs);
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tneg = exp(-sqrt(-1)*freqs);
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hp1 = 4*lambda*(1 - cos(freqs)).^2 ./ (1 + 4*lambda*(1 - cos(freqs)).^2);
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mathp_col = [];
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IA = eye(size(A,1));
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IE = eye(M_.exo_nbr);
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for ig = 1:ngrid
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f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*ghu1;IE]...
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*M_.Sigma_e*[ghu1'*inv(IA-A'*tpos(ig)) ...
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IE]); % state variables
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g_omega = [aa*tneg(ig) bb]*f_omega*[aa'*tpos(ig); bb']; % selected variables
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f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
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mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
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% for ifft
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end;
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% covariance of filtered series
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imathp_col = real(ifft(mathp_col))*(2*pi);
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gamma_y{1} = reshape(imathp_col(1,:),nvar,nvar);
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% autocorrelations
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if nar > 0
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sy = sqrt(diag(gamma_y{1}));
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sy = sy *sy';
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for i=1:nar
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gamma_y{i+1} = reshape(imathp_col(i+1,:),nvar,nvar)./sy;
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end
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end
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%variance decomposition
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if M_.exo_nbr > 1
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gamma_y{nar+2} = zeros(nvar,M_.exo_nbr);
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SS(M_.exo_names_orig_ord,M_.exo_names_orig_ord)=M_.Sigma_e+1e-14*eye(M_.exo_nbr);
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cs = chol(SS)';
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SS = cs*cs';
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b1(:,M_.exo_names_orig_ord) = ghu1;
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b2(:,M_.exo_names_orig_ord) = ghu(iky,:);
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mathp_col = [];
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IA = eye(size(A,1));
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IE = eye(M_.exo_nbr);
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for ig = 1:ngrid
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f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
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*SS*[b1'*inv(IA-A'*tpos(ig)) ...
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IE]); % state variables
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g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
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f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
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mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
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% for ifft
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end;
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imathp_col = real(ifft(mathp_col))*(2*pi);
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vv = diag(reshape(imathp_col(1,:),nvar,nvar));
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for i=1:M_.exo_nbr
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mathp_col = [];
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SSi = cs(:,i)*cs(:,i)';
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for ig = 1:ngrid
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f_omega =(1/(2*pi))*( [inv(IA-A*tneg(ig))*b1;IE]...
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*SSi*[b1'*inv(IA-A'*tpos(ig)) ...
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IE]); % state variables
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g_omega = [aa*tneg(ig) b2]*f_omega*[aa'*tpos(ig); b2']; % selected variables
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f_hp = hp1(ig)^2*g_omega; % spectral density of selected filtered series
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mathp_col = [mathp_col ; (f_hp(:))']; % store as matrix row
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% for ifft
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end;
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imathp_col = real(ifft(mathp_col))*(2*pi);
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gamma_y{nar+2}(:,i) = abs(diag(reshape(imathp_col(1,:),nvar,nvar)))./vv;
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end
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end
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end
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if sscanf(version('-release'),'%d') < 13
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warning on
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else
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eval('warning on MATLAB:dividebyzero')
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end
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% 10/18/2002 MJ
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% 10/30/2002 added autocorrelations, gamma_y is now a cell array
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% 01/20/2003 MJ added variance decomposition
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% 02/18/2003 MJ added HP filtering (Thanks to Jean Chateau for the code)
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% 04/28/2003 MJ changed handling of options
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% 05/19/2003 MJ don't assume lags are in increasing order in building A
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% 05/21/2003 MJ added global i_exo_var_,
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% variance decomposition: test M_.exo_nbr > 1
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% 05/29/2003 MJ removed global i_exo_var_
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% 06/10/2003 MJ test release for warning syntax |