--- /dev/null
+function [FPE,AIC,BIC,SBC,MDL,CATcrit,PHI,optFPE,optAIC,optBIC,optSBC,optMDL,optCAT,optPHI,p,C]=selmo(e,NC);
+% Model order selection of an autoregrssive model
+% [FPE,AIC,BIC,SBC,MDL,CAT,PHI,optFPE,optAIC,optBIC,optSBC,optMDL,optCAT,optPHI]=selmo(E,N);
+%
+% E Error function E(p)
+% N length of the data set, that was used for calculating E(p)
+% show optional; if given the parameters are shown
+%
+% FPE Final Prediction Error (Kay 1987, Wei 1990, Priestley 1981 -> Akaike 1969)
+% AIC Akaike Information Criterion (Marple 1987, Wei 1990, Priestley 1981 -> Akaike 1974)
+% BIC Bayesian Akaike Information Criterion (Wei 1990, Priestley 1981 -> Akaike 1978,1979)
+% CAT Parzen's CAT Criterion (Wei 1994 -> Parzen 1974)
+% MDL Minimal Description length Criterion (Marple 1987 -> Rissanen 1978,83)
+% SBC Schwartz's Bayesian Criterion (Wei 1994; Schwartz 1978)
+% PHI Phi criterion (Pukkila et al. 1988, Hannan 1980 -> Hannan & Quinn, 1979)
+% HAR Haring G. (1975)
+% JEW Jenkins and Watts (1968)
+%
+% optFPE order where FPE is minimal
+% optAIC order where AIC is minimal
+% optBIC order where BIC is minimal
+% optSBC order where SBC is minimal
+% optMDL order where MDL is minimal
+% optCAT order where CAT is minimal
+% optPHI order where PHI is minimal
+%
+% usually is
+% AIC > FPE > *MDL* > PHI > SBC > CAT ~ BIC
+%
+% REFERENCES:
+% P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+% S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
+% M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
+% C.E. Shannon and W. Weaver "The mathematical theory of communication" University of Illinois Press, Urbana 1949 (reprint 1963).
+% W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+% Jenkins G.M. Watts D.G "Spectral Analysis and its applications", Holden-Day, 1968.
+% G. Haring "Über die Wahl der optimalen Modellordnung bei der Darstellung von stationären Zeitreihen mittels Autoregressivmodell als Basis der Analyse von EEG - Biosignalen mit Hilfe eines Digitalrechners", Habilitationschrift - Technische Universität Graz, Austria, 1975.
+% (1)"About selecting the optimal model at the representation of stationary time series by means of an autoregressive model as basis of the analysis of EEG - biosignals by means of a digital computer)"
+%
+
+% $Id: selmo.m 9609 2012-02-10 10:18:00Z schloegl $
+% Copyright (C) 1997-2002,2008,2012 by Alois Schloegl <alois.schloegl@ist.ac.at>
+% This is part of the TSA-toolbox. See also
+% http://pub.ist.ac.at/~schloegl/matlab/tsa/
+% http://octave.sourceforge.net/
+% http://biosig.sourceforge.net/
+%
+% This program 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.
+%
+% This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
+
+[lr,lc]=size(e);
+if (lr>1) && (lc>1),
+ p=zeros(lr+1,9)+NaN;
+else
+ p=zeros(1,9)+NaN;
+end;
+
+if nargin<2
+ NC=lc*ones(lr,1);
+ NC=(lc-sum(isnan(e)')')*(NC<lc) + NC.*(NC>=lc); % first part
+%end;% Pmax=min([100 N/3]); end;
+ %if NC<lc N=lc; end;
+ %NC=(lc-sum(isnan(e)')')*(NC<lc) + NC.*(NC>=lc); % first part
+else
+ % NC=NC;
+end;
+
+M=lc-1;
+m=0:M;
+
+e = e./e(:,ones(1,lc));
+
+for k=0:lr,
+ if k>0, %
+ E=e(k,:);
+ N=NC(k);
+ elseif lr>1
+ tmp = e;%(NC>0,:);
+ tmp(isnan(tmp)) = 0;
+ E = sum(tmp.*(NC*ones(1,lc)))/sum(NC); % weighted average, weigths correspond to number of valid (not missing) values
+ N = sum(NC)./sum(NC>0); % corresponding number of values,
+ else
+ E = e;
+ N = NC;
+ end;
+FPE = E.*(N+m)./(N-m); %OK
+ optFPE=find(FPE==min(FPE))-1; %optimal order
+ if isempty(optFPE), optFPE=NaN; end;
+AIC = N*log(E)+2*m; %OK
+ optAIC=find(AIC==min(AIC))-1; %optimal order
+ if isempty(optAIC), optAIC=NaN; end;
+AIC4=N*log(E)+4*m; %OK
+ optAIC4=find(AIC4==min(AIC4))-1; %optimal order
+ if isempty(optAIC4), optAIC4=NaN; end;
+
+m=1:M;
+BIC=[ N*log(E(1)) N*log(E(m+1)) - (N-m).*log(1-m/N) + m*log(N) + m.*log(((E(1)./E(m+1))-1)./m)];
+%BIC=[ N*log(E(1)) N*log(E(m+1)) - m + m*log(N) + m.*log(((E(1)./E(m+1))-1)./m)];
+%m=0:M; BIC=N*log(E)+m*log(N); % Hannan, 1980 -> Akaike, 1977 and Rissanen 1978
+ optBIC=find(BIC==min(BIC))-1; %optimal order
+ if isempty(optBIC), optBIC=NaN; end;
+
+HAR(2:lc)=-(N-m).*log((N-m).*E(m+1)./(N-m+1)./E(m));
+ HAR(1)=HAR(2);
+ optHAR=min(find(HAR<=(min(HAR)+0.2)))-1; %optimal order
+% optHAR=find(HAR==min(HAR))-1; %optimal order
+ if isempty(optHAR), optHAR=NaN; end;
+
+m=0:M;
+SBC = N*log(E)+m*log(N);
+ optSBC=find(SBC==min(SBC))-1; %optimal order
+ if isempty(optSBC), optSBC=NaN; end;
+MDL = N*log(E)+log(N)*m;
+ optMDL=find(MDL==min(MDL))-1; %optimal order
+ if isempty(optMDL), optMDL=NaN; end;
+
+m=0:M;
+%CATcrit= (cumsum(1./E(m+1))/N-1./E(m+1));
+E1=N*E./(N-m);
+CATcrit= (cumsum(1./E1(m+1))/N-1./E1(m+1));
+ optCAT=find(CATcrit==min(CATcrit))-1; %optimal order
+ if isempty(optCAT), optCAT=NaN; end;
+
+PHI = N*log(E)+2*log(log(N))*m;
+ optPHI=find(PHI==min(PHI))-1; %optimal order
+ if isempty(optPHI), optPHI=NaN; end;
+
+JEW = E.*(N-m)./(N-2*m-1); % Jenkins-Watt
+ optJEW=find(JEW==min(JEW))-1; %optimal order
+ if isempty(optJEW), optJEW=NaN; end;
+
+% in case more than 1 minimum is found, the smaller model order is returned;
+p(k+1,:) = [optFPE(1), optAIC(1), optBIC(1), optSBC(1), optCAT(1), optMDL(1), optPHI(1), optJEW(1), optHAR(1)];
+
+end;
+C=[FPE;AIC;BIC;SBC;MDL;CATcrit;PHI;JEW;HAR(:)']';
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff