113 lines
3.4 KiB
Matlab
113 lines
3.4 KiB
Matlab
function [yy, xdir, isig, lam]=log_transform(y0,xdir0,isig,lam)
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% [yy, xdir, isig, lam]=log_transform(y0,xdir0,isig,lam)
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% Conduct automatic log transformation lam(yy/isig+lam)
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% Inputs:
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% - y0 [double] series to transform
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% - xdir [char] string indating the type of transformation:
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% - log: standard log transformation
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% - minuslog: log of minus (y0)
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% - logsquared: log of y0^2
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% - logskew: log of y0 shifted by lam
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% - isig [double] scaling factor for y0
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% - lam [double] shifting for y0
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%
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% Outputs:
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% - yy [double] transformed series
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% - xdir [char] string indating the type of transformation:
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% - log: standard log transformation
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% - minuslog: log of minus (y0)
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% - logsquared: log of y0^2
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% - logskew: log of y0 shifted by lam
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% - isig [double] scaling factor for y0
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% - lam [double] shifting for y0
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%
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% Notes: takes either one or four arguments. For one argument, the log
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% transformation is conducted. For four arguments, the inverse
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% transformation is applied.
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% Written by Marco Ratto
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% Joint Research Centre, The European Commission,
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% marco.ratto@ec.europa.eu
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% Copyright © 2012 European Commission
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% Copyright © 2012-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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if nargin==4
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% inverse transformation
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yy = (exp(y0)-lam)*isig;
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return
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end
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if nargin==1
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xdir0='';
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end
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f=@(lam,y)gsa.skewness(log(y+lam));
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isig=1;
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if ~(max(y0)<0 || min(y0)>0)
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if gsa.skewness(y0)<0
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isig=-1;
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y0=-y0;
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end
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if isoctave
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n=hist(y0,10);
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else
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n=histcounts(y0,10);
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end
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if n(1)>20*n(end)
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try
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lam=fzero(f,[-min(y0)+10*eps -min(y0)+abs(median(y0))],[],y0);
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catch
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yl(1)=f(-min(y0)+10*eps,y0);
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yl(2)=f(-min(y0)+abs(median(y0)),y0);
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if abs(yl(1))<abs(yl(2))
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lam=-min(y0)+eps;
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else
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lam = -min(y0)+abs(median(y0));
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end
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end
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yy = log(y0+lam);
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xdir=[xdir0,'_logskew'];
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else
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isig=0;
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lam=0;
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yy = log(y0.^2);
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xdir=[xdir0,'_logsquared'];
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end
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else
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if max(y0)<0
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isig=-1;
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y0=-y0;
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xdir=[xdir0,'_minuslog'];
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elseif min(y0)>0
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xdir=[xdir0,'_log'];
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end
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try
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lam=fzero(f,[-min(y0)+10*eps -min(y0)+median(y0)],[],y0);
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catch
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yl(1)=f(-min(y0)+10*eps,y0);
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yl(2)=f(-min(y0)+abs(median(y0)),y0);
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if abs(yl(1))<abs(yl(2))
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lam=-min(y0)+eps;
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else
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lam = -min(y0)+abs(median(y0));
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end
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end
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lam = max(lam,0);
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yy = log(y0+lam);
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end
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