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function [xtx,xty,yty,fss,phi,y,ncoef,xr,Bh,e] = fn_dataxy7982(nvar,lags,z,mu,indxDummy,...
q_m,SpBin,SkipBin,SkipFin,nexo)
% [xtx,xty,yty,fss,phi,y,ncoef,xr,Bh,e] = fn_dataxy7982(nvar,lags,z,mu,indxDummy,...
% q_m,SpBin,SkipBin,SkipFin,nexo)
% Export arranged data matrices for future estimation for DM models with the period from
% SkipBin to SkipFin to be skiped.
% See Wagonner and Zha's Gibbs sampling paper.
%
% nvar: number of endogenous variables.
% lags: the maximum length of lag
% z: T*(nvar+(nexo-1)) matrix of raw or original data (no manipulation involved)
% with sample size including lags and with exogenous variables other than a constant.
% Order of columns: (1) nvar endogenous variables; (2) (nexo-1) exogenous variables;
% (3) constants are automatically put in the last column.
% mu: 6-by-1 vector of hyperparameters (the following numbers for Atlanta Fed's forecast)
% mu(1): overall tightness and also for A0; (0.57)
% mu(2): relative tightness for A+; (0.13)
% mu(3): relative tightness for the constant term; (0.1)
% mu(4): tightness on lag decay; (1)
% mu(5): weight on nvar sums of coeffs dummy observations (unit roots); (5)
% mu(6): weight on single dummy initial observation including constant
% (cointegration, unit roots, and stationarity); (5)
% Here, only mu(5) and mu(6) are used for dummy observations
% indxDummy = 1; % 1: add dummy observations to the data; 0: no dummy added.
% q_m: 12 (monthly) or 4 (quarterly).
% SpBin: [year month] at the begining of the sample (including lags).
% SkipBin: [year month] at the begining of the skipped period.
% SkipFin: [year month] at the end of the skipped period.
% nexo: number of exogenous variables. The constant term is the default setting. Besides this term,
% we have nexo-1 exogenous variables.
% -------------------
% xtx: X'X: k-by-k where k=ncoef
% xty: X'Y: k-by-nvar
% yty: Y'Y: nvar-by-nvar
% fss: T: sample size excluding lags. With dummyies, fss=nSample-lags+ndobs.
% phi: X; T-by-k; column: [nvar for 1st lag, ..., nvar for last lag, other exogenous terms, const term]
% y: Y: T-by-nvar where T=fss
% ncoef: number of coefficients in *each* equation. RHS coefficients only, nvar*lags+nexo
% xr: the economy size (ncoef-by-ncoef) in qr(phi) so that xr=chol(X'*X) or xr'*xr=X'*X
% Bh: ncoef-by-nvar estimated reduced-form parameter; column: nvar;
% row: ncoef=[nvar for 1st lag, ..., nvar for last lag, other exogenous terms, const term]
% e: estimated residual e = y -x*Bh, T-by-nvar
%
% Tao Zha, February 2000. Revised, May 2001.
% See fn_dataxy.m.
%
% Copyright (C) 1997-2012 Tao Zha
%
% This free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% It is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% If you did not received a copy of the GNU General Public License
% with this software, see <http://www.gnu.org/licenses/>.
%
if nargin == 9
nexo=1; % default for constant term
elseif nexo<1
error('We need at least one exogenous term so nexo must >= 1')
end
%*** original sample dimension without dummy prior
nSample = size(z,1); % the sample size (including lags, of course)
sb = lags+1; % original beginning without dummies
ncoef = nvar*lags+nexo; % number of coefficients in *each* equation, RHS coefficients only.
if indxDummy % prior dummy prior
%*** expanded sample dimension by dummy prior
ndobs=nvar+1; % number of dummy observations
fss = nSample+ndobs-lags;
%
% **** nvar prior dummy observations with the sum of coefficients
% ** construct X for Y = X*B + U where phi = X: (T-lags)*k, Y: (T-lags)*nvar
% ** columns: k = # of [nvar for 1st lag, ..., nvar for last lag, exo var, const]
% ** Now, T=T+ndobs -- added with "ndobs" dummy observations
%
phi = zeros(fss,ncoef);
%* constant term
const = ones(fss,1);
const(1:nvar) = zeros(nvar,1);
phi(:,ncoef) = const; % the first nvar periods: no or zero constant!
%* other exogenous (than) constant term
phi(ndobs+1:end,ncoef-nexo+1:ncoef-1) = z(lags+1:end,nvar+1:nvar+nexo-1);
exox = zeros(ndobs,nexo);
phi(1:ndobs,ncoef-nexo+1:ncoef-1) = exox(:,1:nexo-1);
% this = [] when nexo=1 (no other exogenous than constant)
xdgel = z(:,1:nvar); % endogenous variable matrix
xdgelint = mean(xdgel(1:lags,:),1); % mean of the first lags initial conditions
%* Dummies
for k=1:nvar
for m=1:lags
phi(ndobs,nvar*(m-1)+k) = xdgelint(k);
phi(k,nvar*(m-1)+k) = xdgelint(k);
% <<>> multiply hyperparameter later
end
end
%* True data
for k=1:lags
phi(ndobs+1:fss,nvar*(k-1)+1:nvar*k) = xdgel(sb-k:nSample-k,:);
% row: T-lags; column: [nvar for 1st lag, ..., nvar for last lag, exo var, const]
% Thus, # of columns is nvar*lags+nexo = ncoef.
end
%
% ** Y with "ndobs" dummies added
y = zeros(fss,nvar);
%* Dummies
for k=1:nvar
y(ndobs,k) = xdgelint(k);
y(k,k) = xdgelint(k);
% multiply hyperparameter later
end
%* True data
y(ndobs+1:fss,:) = xdgel(sb:nSample,:);
phi(1:nvar,:) = 1*mu(5)*phi(1:nvar,:); % standard Sims and Zha prior
y(1:nvar,:) = mu(5)*y(1:nvar,:); % standard Sims and Zha prior
phi(nvar+1,:) = mu(6)*phi(nvar+1,:);
y(nvar+1,:) = mu(6)*y(nvar+1,:);
%-------------- Taking the 79:10-83:12 period out ----------------------
outper1=(SkipBin(1)-SpBin(1))*q_m+(SkipBin(2)-SpBin(2)+1) + ndobs-lags;
outper2=(SkipFin(1)-SpBin(1))*q_m+(SkipFin(2)-SpBin(2)+1) + ndobs-lags;
phi(outper1:outper2,:)=[];
y(outper1:outper2,:)=[];
fss=size(phi,1);
[xq,xr]=qr(phi,0);
xtx=xr'*xr;
xty=phi'*y;
[yq,yr]=qr(y,0);
yty=yr'*yr;
Bh = xr\(xr'\xty); % xtx\xty where inv(X'X)*(X'Y)
e=y-phi*Bh;
else
fss = nSample-lags;
%
% ** construct X for Y = X*B + U where phi = X: (T-lags)*k, Y: (T-lags)*nvar
% ** columns: k = # of [nvar for 1st lag, ..., nvar for last lag, exo var, const]
%
phi = zeros(fss,ncoef);
%* constant term
const = ones(fss,1);
phi(:,ncoef) = const; % the first nvar periods: no or zero constant!
%* other exogenous (than) constant term
phi(:,ncoef-nexo+1:ncoef-1) = z(lags+1:end,nvar+1:nvar+nexo-1);
% this = [] when nexo=1 (no other exogenous than constant)
xdgel = z(:,1:nvar); % endogenous variable matrix
%* True data
for k=1:lags
phi(:,nvar*(k-1)+1:nvar*k) = xdgel(sb-k:nSample-k,:);
% row: T-lags; column: [nvar for 1st lag, ..., nvar for last lag, exo var, const]
% Thus, # of columns is nvar*lags+nexo = ncoef.
end
%
y = xdgel(sb:nSample,:);
%-------------- Taking the 79:10-83:12 period out ----------------------
outper1=(SkipBin(1)-SpBin(1))*q_m+(SkipBin(2)-SpBin(2)+1) - lags;
outper2=(SkipFin(1)-SpBin(1))*q_m+(SkipFin(2)-SpBin(2)+1) - lags;
phi(outper1:outper2,:)=[];
y(outper1:outper2,:)=[];
fss=size(phi,1);
[xq,xr]=qr(phi,0);
xtx=xr'*xr;
xty=phi'*y;
[yq,yr]=qr(y,0);
yty=yr'*yr;
Bh = xr\(xr'\xty); % xtx\xty where inv(X'X)*(X'Y)
e=y-phi*Bh;
end
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