acovf.m

MATLAB的时间序列分析相关函数,涵盖对时间序列分析所需要所有重要函数

function [ACF,NN] = acovf(Z,KMAX,Mode,Mode2);
% ACOVF estimates autocovariance function (not normalized)
% NaN's are interpreted as missing values. 
%
% [ACF,NN] = acovf(Z,MAXLAG,Mode);
%
% Input:
%  Z    Signal (one channel per row);
%  MAXLAG  maximum lag
%  Mode	'biased'  : normalizes with N
%	'unbiased': normalizes with N-lag
%	'coeff'	  : normalizes such that lag 0 is 1	
%        others	  : no normalization
%
% Output:
%  ACF autocovariance function
%  NN  number of valid elements 
%
%
% REFERENCES:
%  A.V. Oppenheim and R.W. Schafer, Digital Signal Processing, Prentice-Hall, 1975.
%  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.

%	$Id: acovf.m 5090 2008-06-05 08:12:04Z schloegl $
%       Copyright (C) 1998-2003,2008 by Alois Schloegl <[e-mail]>
%
%    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/>.



if nargin<3, Mode='biased'; end;

[lr,lc] = size(Z);

MISSES = sum(isnan(Z)')';
if any(MISSES); % missing values
	M = real(~isnan(Z));
	Z(isnan(Z))=0;
end;

if (nargin == 1) 
	KMAX = lc-1; 
elseif (KMAX >= lc-1) 
	KMAX = lc-1;
end;

ACF = zeros(lr,KMAX+1);

if nargin>3,		% for testing, use arg4 for comparing the methods,

elseif 	(KMAX*KMAX > lc*log2(lc)) % & isempty(MISSES);	
	Mode2 = 1;
elseif 	(10*KMAX > lc);
	Mode2 = 3;
else
	Mode2 = 4;
end;


%%%%% ESTIMATION of non-normalized ACF %%%%%

% the following algorithms gve equivalent results, however, the computational effort is different,
% depending on lr,lc and KMAX, a different algorithm is most efficient.
if Mode2==1; % KMAX*KMAX > lc*log(lc);        % O(n.logn)+O(K