# R/S分析Matlab程序

function [logRS,logERS,V]=RSana(x,n,method,q)
% Alexandros Leontitsis
% Department of Education
% University of Ioannina
% 45110 - Dourouti
% Ioannina
% Greece
%
% University e-mail: me00743@cc.uoi.gr
% Homepage: http://www.geocities.com/CapeCanaveral/Lab/1421
%
% 1 Jan 2004.

if nargin<1 | isempty(x)==1
error('You should provide a time series.');
else
% x must be a vector
if min(size(x))>1
error('Invalid time series.');
end
x=x(:);
% N is the time series length
N=length(x);
end

if nargin<2 | isempty(n)==1
n=1;
else
% n must be either a scalar or a vector
if min(size(n))>1
error('n must be either a scalar or a vector.');
end
% n must be integer
if n-round(n)~=0
error('n must be integer.');
end
% n must be positive
if n<=0
error('n must be positive.');
end
end

if nargin<4 | isempty(q)==1
q=0;
else
if q=='auto'
t=autocorr(x,1);
t=t(2);
q=((3*N/2)^(1/3))*(2*t/(1-t^2))^(2/3);
else
% q must be a scalar
if sum(size(q))>2
error('q must be scalar.');
end
% q must be integer
if q-round(q)~=0
error('q must be integer.');
end
% q must be positive
if q<0
error('q must be positive.');
end
end
end

for i=1:length(n)

% Calculate the sub-periods
a=floor(N/n(i));

% Make the sub-periods matrix
X=reshape(x(1:a*n(i)),n(i),a);

% Estimate the mean of each sub-period
ave=mean(X);

% Remove the mean from each sub-period
cumdev=X-ones(n(i),1)*ave;

% Estimate the cumulative deviation from the mean
cumdev=cumsum(cumdev);

% Estimate the standard deviation
switch method
case 'Hurst'
% Hurst-Mandelbrot variation
stdev=std(X);
case 'Lo'
% Lo variation
for j=1:a
sq=0;
for k=0:q
v(k+1)=sum(X(k+1:n(i),j)'*X(1:n(i)-k,j))/(n(i)-1);
if k>0
sq=sq+(1-k/(q+1))*v(k+1);
end
end
stdev(j)=sqrt(v(1)+2*sq);
end
case 'MW'
% Moody-Wu variation
for j=1:a
sq1=0;
sq2=0;
for k=0:q
v(k+1)=sum(X(k+1:n(i),j)'*X(1:n(i)-k,j))/(n(i)-1);
if k>0
sq1=sq1+(1-k/(q+1))*(n(i)-k)/n(i)/n(i);
sq2=sq2+(1-k/(q+1))*v(k+1);
end
end
stdev(j)=sqrt((1+2*sq1)*v(1)+2*sq2);
end
case 'Parzen'
% Parzen variation
if mod(q,2)~=0
error('For the "Parzen" variation q must be dived by 2.');
end
for j=1:a
sq1=0;
sq2=0;
for k=0:q
v(k+1)=sum(X(k+1:n(i),j)'*X(1:n(i)-k,j))/(n(i)-1);
if k>0 & k<=q/2
sq1=sq1+(1-6*(k/q)^2+6*(k/q)^3)*v(k+1);
elseif k>0 & k>q/2
sq2=sq2+(1-(k/q)^3)*v(k+1);
end
end
stdev(j)=sqrt(v(1)+2*sq1+2*sq2);
end
otherwise
error('You should provide another value for "method".');
end

% Estiamte the rescaled range
rs=(max(cumdev)-min(cumdev))./stdev;

clear stdev

% Take the logarithm of the mean R/S
logRS(i,1)=log10(mean(rs));

if nargout>1

% Initial calculations fro the log(E(R/S))
j=1:n(i)-1;
s=sqrt((n(i)-j)./j);
s=sum(s);

% The estimation of log(E(R/S))
logERS(i,1)=log10(s/sqrt(n(i)*pi/2));

% Other estimations of log(E(R/S))
%logERS(i,1)=log10((n(i)-0.5)/n(i)*s/sqrt(n(i)*pi/2));
%logERS(i,1)=log10(sqrt(n(i)*pi/2));

end

if nargout>2
% Estimate V
V(i,1)=mean(rs)/sqrt(n(i));
end
end

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