Measuring the Effects of a Shock to Monetary Policy - Humboldt ...

98 Bayesian FAVARs with Agnostic Identification
%%%%% start kalman filter
% Setting Dimensions
[T,var] = size(Y_Data);
[H_row,H_col] = size(H_Prior); % has to equal size of Lam_bar
[Xsi_row,Xsi_col] = size(Xsi_Prior);
[G_row,G_col] = size(G_Prior);
[Q_row,Q_col] = size(Q_Prior);
[R_row,R_col] = size(R_Prior);
km = Xsi_col/13;
kmd = Xsi_col;
%Variables for State-Space
Y_t = Y_Data;
H_t = H_Prior;
G = G_Prior;
R = R_Prior;
Q = Q_Prior;
vecQ = reshape(Q,Q_row^2,1);
% Sequence of draws to be stored in Xsi_all and P_all
Xsi_all = zeros(T,((K+M)*d));
P_all = zeros(((K+M)*d)^2,T);
%invI = inv(eye(size(Xsi_Prior,1)^2) - kron(G,G));
%vecP_Prior = invI * vecQ;
%P_Prior = reshape(vecP_Prior,size(Xsi_row,1),size(Xsi_row,1));
% Initialization the state vectors variance-covariance matrix
%Xsi_Prior = zeros(Xsi_row,1); % could be taken in case of no initial value
%P_Prior = eye(Xsi_row); % could be taken in case of no initial value
Xsi_tlag = Xsi_Prior;
P_tlag = P_Prior;
% Final Draws to be stored in Xsi_F and P_F
Xsi_F = zeros(Xsi_row,Xsi_col);
P_F = zeros(Xsi_row^2,T);
for t=1:T
%=======================================================%
% Updating equations (Kim&Nelson) %
%*******************************************************%
Eta_tlag = Y_t(t,:)’ - H_t * Xsi_tlag(1:(K+M)); %
f_tlag = H_t * P_tlag(1:(K+M),1:(K+M)) * H_t’ + R;%
if_tlag = inv(f_tlag); %
%if_tlag = pinv(f_tlag); %
K_t = P_tlag(:,1:(K+M)) * H_t’ * if_tlag; %
% %
Xsi_tt = Xsi_tlag + K_t * Eta_tlag; %
P_tt = P_tlag - K_t * H_t * P_tlag(1:(K+M),:); %
%=======================================================%
%-------------------------------------------------------%
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% Prediction equation (Kim&Nelson) %
%*******************************************************%