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function [HDratio,HDvalue,yhatn,yforen] = history2(HDindx,A0,Bhml,phil,nn,...
actup,Estrexa,xdata,nvar,nSample,nSampleCal,forep,forepq,forepy,q_m,...
qmEnd,vlist,vlistlog,vlistper,lmqyIndx)
% [HDratio,HDvalue,yhatn,yforen] = history2(HDindx,A0,Bhml,phil,nn,actup,...
% xdata,nvar,nSample,nSampleCal,forep,forepq,forepy,q_m,...
% qmEnd,vlist,vlistlog,vlistper,lmqyIndx)
%
% (Out-of-sample) historical decompostions: alternative approach to history.m in 3 aspects
% (1) compute the percentage (not the value itself)
% (2) NOT cumulative HD (THIS is NOT correct, TAZ, 03/17/99)
% (3) conditional on time t (not time 0).
% (4) condtional and uncondtional forecasts
%
% HDindx: k-by-1 cell where k groups of shocks; index number for particular shocks
% A0h: nvar-by-nvar for y(t)A0 = X*A+ + E, where column means equation
% Bh: the (posterior) estimate of B for y(t) = X*Bh + E*inv(A0)
% phil: the 1-by-(nvar*lags+1) data matrix where k=nvar*lags+1
% (last period plus lags before the beginning of forecast)
% nn: [nvar,lags,forep], forep: forecast periods (monthly)
% actup: actual data periods (monthly) before the beginning of forecasts
% xdata: oringal data set, up to the period before (peudo-) out-of-sample forecasting,
% all logged except R, U, etc.
% Estrexa: forep-by-nvar -- backed out structural shocks for out-of-sample forecast
% nvar: number of variables
% nSample: sample size (including lags or initial periods)
% nSampleCal: sample size in terms of calendar years
% forep: forecast periods (monthly)
% forepq: forecast periods (quarterly)
% forepy: forecast periods (yearly)
% q_m: quarterly or monthly for the underlying model
% qmEnd: last q_m before out-of-sample forecasting
% vlist: a list of variables
% vlistlog: sub list of variables that are in log
% vlistper: sub list of variables that are in percent
% lmyqIndx: 4-by-1 1 or 0's. Index for m log, m level, qg, and yg; 1: yes; 0: no;
% if lmyqIndx(1)==1, both monthly log and monthly level are returned
%--------------
% HDratio: 5-by-k cells, where k groups (see HDindx) of shocks associated with decomposition;
% 5: monthly log, monthly level, mg, qg, and calendar yg in this order;
% each cell is forep(q)(y)-by-nvar
% HDvalue: same dimension as HDratio but with the values (differences between
% conditional and unconditional forecasts
% yhatn: same dimension as HDratio but with conditional forecasts
% yforen: 5-by-1 cells and each cell is forep(q)(y)-by-nvar unconditional forecasts
%
% October 1998 by Tao Zha.
% Last change 3/19/99 on the dimension of "Estrexa" so that previous programs may not be
% compatible.
%
% 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/>.
%
nyout = 1+nargout('fore_cal');
% +1 because we want the original logged variables as well.
[nHD,jnk] = size(HDindx);
yhat=cell(nHD,1);
yhatn = cell(nyout,nHD);
% row: output such as l, mg, qg, or yg; column: how many decomps
%--------------------------------------------------------------------------
% Unconditional point forecasts for log, monthly levle, mg, qg, and yg.
%--------------------------------------------------------------------------
yforeml = forecast(Bhml,phil,nn);
yforen = cell(nyout,1);
yforen{1} = yforeml;
oputstr = '['; % output string
for n=2:nyout
if n<nyout
oputstr = [oputstr 'yforen{' num2str(n) '},'];
else
oputstr = [oputstr 'yforen{' num2str(n) '}'];
end
end
oputstr =[oputstr ']'];
%
eval([oputstr ' = fore_cal(yforeml,xdata,nvar,nSample,nSampleCal,forep,'...
'forepq,forepy,q_m,qmEnd,vlist,vlistlog,vlistper,lmqyIndx);']);
%--------------------------------------------------------------------------
% Conditional forecasts on specified paths of shocks
% for log, monthly levle, mg, qg, and yg.
%--------------------------------------------------------------------------
for k=1:nHD
Estr = zeros(forep,nvar); % out of sample
Estr(:,HDindx{k}) = Estrexa(:,HDindx{k}); % out of sample, MS
yhat{k} = forefixe(A0,Bhml,phil,nn,Estr);
yhatn{1,k} = yhat{k}; % original logged variables
%
oputstr = '['; % output string
for n=2:nyout
if n<nyout
oputstr = [oputstr 'yhatn{' num2str(n) ',k},'];
else
oputstr = [oputstr 'yhatn{' num2str(n) ',k}'];
end
end
oputstr =[oputstr ']'];
%
eval([oputstr ' = fore_cal(yhat{k},xdata,nvar,nSample,nSampleCal,forep,'...
'forepq,forepy,q_m,qmEnd,vlist,vlistlog,vlistper,lmqyIndx);']);
end
%--------------------------------------------------------------------------
% Historical decompositions: both values and raitos (%)
%--------------------------------------------------------------------------
HDratio=cell(nyout,nHD);
HDvalue=HDratio;
for n=2:nyout
if lmqyIndx(n-1)
if (n-1==1)
yhatotal = zeros(size(yhatn{1,k}));
for k=1:nHD
HDvalue{1,k} = yhatn{1,k}-yforen{1};
yhatotal = yhatotal + abs(HDvalue{1,k});
% a sum of absolute values. One can also use square
end
%
for k=1:nHD
HDratio{1,k} = abs(HDvalue{1,k})*100 ./ yhatotal;
end
end
%
yhatotal = zeros(size(yhatn{n,k}));
for k=1:nHD
HDvalue{n,k} = yhatn{n,k}-yforen{n};
yhatotal = yhatotal + abs(HDvalue{n,k});
% a sum of absolute values. One can also use square
end
%
for k=1:nHD
HDratio{n,k} = abs(HDvalue{n,k})*100 ./ yhatotal;
end
end
end
%** check. This first may not be zeros, but the second (monthly log) must be zeros.
%HDvalue{5,1}+HDvalue{5,2}-...
% (yactCalyg(size(yactCalyg,1)-3:size(yactCalyg,1),:)-yforeCalygml)
%HDvalue{1,1}+HDvalue{1,2}-...
% (yact(size(yact,1)-forep+1:size(yact,1),:)-yforen{1,1})
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