function [AUTOCOV,stderr,lpq,qpval] = acorf(Z,N);%  Calculates autocorrelations for multiple data series.%  Missing values in Z (NaN) are considered. %  Also calculates Ljung-Box Q stats and p-values.%%    [AutoCorr,stderr,lpq,qpval] = acorf(Z,N);%  If mean should be removed use%    [AutoCorr,stderr,lpq,qpval] = acorf(detrend(Z',0)',N);%  If trend should be removed use%    [AutoCorr,stderr,lpq,qpval] = acorf(detrend(Z')',N);%% INPUT%  Z	is data series for which autocorrelations are required%       each in a row%  N	maximum lag%% OUTPUT%  AutoCorr nr x N matrix of autocorrelations%  stderr   nr x N matrix of (approx) std errors%  lpq      nr x M matrix of Ljung-Box Q stats%  qpval    nr x N matrix of p-values on Q stats%   % All input and output parameters are organized in rows, one row % corresponds to one series%% REFERENCES:%  S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.%  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. %  W.S. Wei "Time Series Analysis" Addison Wesley, 1990.%  J.S. Bendat and A.G.Persol "Random Data: Analysis and Measurement procedures", Wiley, 1986.%       Version 2.99a       Date: 13 Jul 2002%	Copyright (C) 1998-2002 by Alois Schloegl <a.schloegl@ieee.org>		% 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);NC = sum(~isnan(Z),2); % missing valuesAUTOCOV = acovf(Z,N);AUTOCOV = AUTOCOV(:,2:N+1) ./ AUTOCOV(:,ones(1,N));if nargout > 1         stderr = sqrt(1./NC)*ones(1,N);        lpq = zeros(nr,N);        qpval = zeros(nr,N);                cum=zeros(nr,1);        for k=1:N,                cum = cum+AUTOCOV(:,k).*conj(AUTOCOV(:,k))./(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                qpval(:,k) = 1 - gammainc(lpq(:,k)/2,k/2);	% replace chi2cdf by gammainc        end;end;