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author | schloegl |
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date | Thu, 02 Apr 2015 10:00:34 +0000 |
parents | 18ff3d258eea |
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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. % calculating lpq, stderr, qpval from % suggested by Philip Gray, University of New South Wales, % $Id$ % Copyright (C) 1998-2002,2008 by Alois Schloegl <alois.schloegl@gmail.com> % % 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/>. [nr,nc] = size(Z); NC = sum(~isnan(Z),2); % missing values AUTOCOV = 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;