rsana.m

用R/S估算法计算时间序列的HURST指数

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function [logRS,logERS,V]=RSana(x,n,method,q) 
%Syntax: [logRS,logERS,V]=RSana(x,n,method,q) 
%____________________________________________ 
% 
% Performs R/S analysis on a time series. 
% 
% logRS is the log(R/S). 
% logERS is the Expectation of log(R/S). 
% V is the V statistic. 
% x is the time series. 
% n is the vector with the sub-periods. 
% method can take one of the following values 
% 'Hurst' for the Hurst-Mandelbrot variation. 
% 'Lo' for the Lo variation. 
% 'MW' for the Moody-Wu variation. 
% 'Parzen' for the Parzen variation. 
% q can be either 
% a (non-negative) integer. 
% 'auto' for the Lo's suggested value. 
% 
% 
% References: 
% 
% Peters E (1991): Chaos and Order in the Capital Markets. Willey 
% 
% Peters E (1996): Fractal Market Analysis. Wiley 
% 
% Lo A (1991): Long term memory in stock market prices. Econometrica 
% 59: 1279-1313 
% 
% Moody J, Wu L (1996): Improved estimates for Rescaled Range and Hurst 
% exponents. Neural Networks in Financial Engineering, eds. Refenes A-P 
% Abu-Mustafa Y, Moody J, Weigend A: 537-553, Word Scientific 
% 
% Hauser M (1997): Semiparametric and nonparametric testing for long 
% memory: A Monte Carlo study. Empirical Economics 22: 247-271 
% 
% 
% Alexandros Leontitsis 
% Department of Education 
% University of Ioannina 
% 45110 - Dourouti 
% Ioannina 
% Greece 
% 
% University e-mail: [e-mail] 
% Lifetime e-mail: [e-mail] 
% 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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