hurst.m

另一种赫斯特指数的算法

clear
% B=normrnd(0,1,1,1024)
% B=B+5
% y=B(1:1024)
load z.mat%待分析数据
y=z(1:1024)
t=length(y)
for i=1:t %计算各个时间标度的平均值
    PJ(i)=sum(y(1:i))/i
end
for i=1:t %计算累计离差
    X=0
    for ii=1:i
        X(ii)=sum(y(1:ii))-PJ(i)*ii
    end
    R(i)=max(X)-min(X)
end
for i=1:t
    S(i)=std(y(1:i))
% YY=y(1:i)-PJ(i)
% YYY=YY.^2
% S(i)=(sum(YYY)/i)^0.5    
    RS(i)=R(i)/S(i)
end
RS_log=log(RS(3:t))
t_log=log(3:t)
P=polyfit(t_log,RS_log,1)%最小二乘法拟合数据
xx=[floor(min(t_log)):ceil(max(t_log))]
yy=P(1)*xx+P(2)
plot(xx,yy)
hold on
plot(t_log,RS_log,'.')
grid on