acorf.m

时间序列工具箱

function [ACF,stderr,lpq,qpval] = acorf(Z,N);
% Autocorrelation function 
%  Calculates autocorrelations for multiple data series.
%  Also calculates Ljung-Box Q stats and p-values.
%
%    [ACF,stderr,lpq,qpval] = acorf(Z,KMAX);
%  If mean should be removed use
%    [ACF,stderr,lpq,qpval] = acorf(detrend(Z',0)',KMAX);
%
% INPUT
%  Z	is data series for which autocorrelations are required
%       each in a row
%  KMAX	is the number of autocorrelations to be calculated
%
% OUTPUT
%  ACF      nr x KMAX matrix of autocorrelations
%  stderr   nr x KMAX matrix of (approx) std errors
%  lpq      nr x KMAX matrix of Ljung-Box Q stats
%  qpval    nr x KMAX matrix of p-values on Q stats
%   
% All input and output parameters are organized in rows, one row 
% corresponds to one series

%	Version 2.44
%	last revision 19.06.1998
%	Copyright (c) 1997, 1998 by Alois Schloegl
%	e-mail: [e-mail]	

% calculating lpq, stderr, qpval from 
% suggested by Philip Gray, University of New South Wales, 

% 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.

[nr,nc]=size(Z);
ACF=acovf(Z,N);
ACF = ACF(:,2:N+1) ./ ACF(:,ones(1,N));

if nargout > 1 

stderr=ones(nr,N)*sqrt(1/nc);
lpq=zeros(nr,N);
qpval=zeros(nr,N);

cum=zeros(nr,1);
for k=1:N,
        cum=cum+ACF(:,k).^2/(nc-k);
        lpq(:,k)=nc*(nc+2)*cum;                 % Ljung box Q for k lags
        qpval(:,k)=1-chi2cdf(lpq(:,k),k);	% p-value of Q stat
end;
end;