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function [yy, xdir, isig, lam]=log_transform(y0,xdir0,isig,lam)
% [yy, xdir, isig, lam]=log_transform(y0,xdir0,isig,lam)
% Conduct automatic log transformation lam(yy/isig+lam)
% Inputs:
% - y0 [double] series to transform
% - xdir [char] string indating the type of transformation:
% - log: standard log transformation
% - minuslog: log of minus (y0)
% - logsquared: log of y0^2
% - logskew: log of y0 shifted by lam
% - isig [double] scaling factor for y0
% - lam [double] shifting for y0
%
% Outputs:
% - yy [double] transformed series
% - xdir [char] string indating the type of transformation:
% - log: standard log transformation
% - minuslog: log of minus (y0)
% - logsquared: log of y0^2
% - logskew: log of y0 shifted by lam
% - isig [double] scaling factor for y0
% - lam [double] shifting for y0
%
% Notes: takes either one or four arguments. For one argument, the log
% transformation is conducted. For four arguments, the inverse
% transformation is applied.
% Written by Marco Ratto
% Joint Research Centre, The European Commission,
% marco.ratto@ec.europa.eu
% Copyright © 2012 European Commission
% Copyright © 2012-2017 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is 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.
%
% Dynare 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.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
if nargin==4
% inverse transformation
yy = (exp(y0)-lam)*isig;
return
end
if nargin==1
xdir0='';
end
f=@(lam,y)gsa.skewness(log(y+lam));
isig=1;
if ~(max(y0)<0 || min(y0)>0)
if gsa.skewness(y0)<0
isig=-1;
y0=-y0;
end
if isoctave
n=hist(y0,10);
else
n=histcounts(y0,10);
end
if n(1)>20*n(end)
try
lam=fzero(f,[-min(y0)+10*eps -min(y0)+abs(median(y0))],[],y0);
catch
yl(1)=f(-min(y0)+10*eps,y0);
yl(2)=f(-min(y0)+abs(median(y0)),y0);
if abs(yl(1))<abs(yl(2))
lam=-min(y0)+eps;
else
lam = -min(y0)+abs(median(y0));
end
end
yy = log(y0+lam);
xdir=[xdir0,'_logskew'];
else
isig=0;
lam=0;
yy = log(y0.^2);
xdir=[xdir0,'_logsquared'];
end
else
if max(y0)<0
isig=-1;
y0=-y0;
xdir=[xdir0,'_minuslog'];
elseif min(y0)>0
xdir=[xdir0,'_log'];
end
try
lam=fzero(f,[-min(y0)+10*eps -min(y0)+median(y0)],[],y0);
catch
yl(1)=f(-min(y0)+10*eps,y0);
yl(2)=f(-min(y0)+abs(median(y0)),y0);
if abs(yl(1))<abs(yl(2))
lam=-min(y0)+eps;
else
lam = -min(y0)+abs(median(y0));
end
end
lam = max(lam,0);
yy = log(y0+lam);
end
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