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function [probelow,valow,yhatmean] = probvalsec(yhatprob,yhatpo,ninv,forep,nvar,findex,...
sindex,valix,prolix)
% [probelow,valow,yhatmean] = probvalsec(yhatprob,yhatpo,ninv,forep,nvar,findex,...
% sindex,valix,prolix)
%
% Probabilites (below) and values for selected variables and levels.
% This program takes outputs from "histpdfcnt.m" which must be run first.
% Compute (1) the probability of the x-value (such as FFR) that is below a level
% prespecified by valix (e.g., probability of R below 5%); (2) the x-value
% (such as median or .60 lower-tail value) below which the probability is at a level
% prespecified by "prolix" (e.g., median when 0.50 is prespecified); (3) the mean
% of the x-values (e.g., the mean of Pcm, M2, FFR, etc.).
%
% yhatprob: 2+ninv-by-forep*shockp(=1 here)*nvar. Probability (NOT density) at each bin
% yhatpo: 2+ninv-by-forep*shockp(=1 here)*nvar. Bin position (x-axis) in relation to yhat
% ninv: the number of bins which are small interior intervals on the x-axis
% forep: forecast periods -- 1st dim (must be compatible with findex)
% nvar: number of shocks or variables -- 2nd dim (must be compatible with sindex)
% findex: index for sected forecast periods 1st dim (c.f., forep)
% sindex: index for selected shocks or variables, 2nd dim (c.f., nvar)
% valix: length(findex)-by-length(sindex). Selected values on the x-axis
% prolix: length(findex)-by-length(sindex). Selected (below) probabilites
%-----------
% probelow: length(findex)-by-length(sindex). The probability of the x-value
% (such as FFR) that is below a level prespecified by valix (e.g.,
% probability of R below 5%).
% valow: length(findex)-by-length(sindex). The x-value (such as median or .60
% lower-tail value) below which the probability is at a level
% prespecified by "prolix" (e.g., median when 0.50 is prespecified);
% yhatmean: forep-by-nvar. The mean of forecasts of Pcm, M2, FFR, etc.
%
% 3/25/99 Tao A. Zha
%
% 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/>.
%
yhatprob2=reshape(yhatprob,2+ninv,forep,nvar);
yhatpo2=reshape(yhatpo,2+ninv,forep,nvar);
%
%** Mean
yhatmean0 = sum(yhatprob.*yhatpo,1);
yhatmean = reshape(yhatmean0,forep,nvar);
%
probelow=zeros(length(findex),length(sindex));
% probablity of the x-value that is below a specified level
% E.g., probability of R below 5%.
valow=probelow;
% x-value for the probability that is below a specified level
% E.g., median when 0.50 is specified.
cumprob=cumsum(yhatprob2,1); % cumulative probabilities
%
count1=0;
for k1=sindex % forecast variables (or shocks)
count1=count1+1;
count2=0;
for k2=findex % forecast periods
count2=count2+1;
posix = max(find(yhatpo2(:,k2,k1)<valix(count2,count1)));
% index for the position corr. to the x-value respeicied.
if isempty(posix)
probelow(count2,count1) = cumprob(1,k2,k1);
else
probelow(count2,count1) = cumprob(posix,k2,k1);
end
posix1 = max(find(cumprob(:,k2,k1)<prolix(count2,count1)));
% index for the position corr. probability (below) specified.
if isempty(posix1)
valow(count2,count1) = yhatpo2(1,k2,k1);
else
valow(count2,count1) = yhatpo2(posix1,k2,k1);
end
end
end
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