www.gusucode.com > 时间序列分析工具箱 - tsa源码程序 > tsa/selmo.m
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 "躡er die Wahl der optimalen Modellordnung bei der Darstellung von station鋜en Zeitreihen mittels Autoregressivmodell als Basis der Analyse von EEG - Biosignalen mit Hilfe eines Digitalrechners", Habilitationschrift - Technische Universit鋞 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)"
%
%
% (1) engl. translation of the titel by A. Schloegl
% Version 2.99b
% last revision 01.10.2002
% Copyright (C) 1997-2002 by Alois Schloegl <a.schloegl@ieee.org>
% This library is free software; you can redistribute it and/or
% modify it under the terms of the GNU Library General Public
% License as published by the Free Software Foundation; either
% Version 2 of the License, or (at your option) any later version.
%
% This library 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
% Library General Public License for more details.
%
% You should have received a copy of the GNU Library General Public
% License along with this library; if not, write to the
% Free Software Foundation, Inc., 59 Temple Place - Suite 330,
% Boston, MA 02111-1307, USA.
[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(:)']';