Continuous research on the trend of stock index (Hurst index)

Only the basic suitable for small white MATLAB Implementation code, in-depth research in addition to the need to improve the algorithm, I suggest a good study of chaos and fractal, do not say let you grasp the trend, at least not big loss, this capital profit and loss callback I have studied before.

function [line_h,rs]=dfax_0322 (x)
Percent-of-initialization data processing
% x=importdata (' IF.txt '); [line_h,rs]=dfax_0322 (x); line_h
%x=1000*rand (4000,1); [line_h,rs]=dfax_0322 (x); line_h
X=x (:); x=x+2;% prevent 0 in X
X1=log ([X (2:end)])-log (x); x=x1 (1:end-1);% elimination of short-term autocorrelation of sequences to meet the requirements of R/S analysis for observing objects independently
% X=cumsum (X-mean (x));
%x=log (x (:));
N=length (x);
Xulie=[8:floor (N/2)];% means dividing X into floor (N/xulie (i)) segment

Percent processing input

Len_xulie=length (Xulie);
Rs=zeros (1,len_xulie);% initialization sequence with a bad mark

Percent of the RS process
For Flag_i=1:len_xulie
M=xulie (flag_i);
Junzhi_ij=zeros (1,floor (N/xulie (flag_i)));% initialization mean
Biaozhuencha_ij=zeros (1,floor (N/xulie (flag_i)));% Initialization standard deviation
Jicha_ij=zeros (1,floor (N/xulie (flag_i))),% initialization very poor
For Flag_j=1:floor (N/xulie (flag_i))
Yuansu_ij=x ([m* (Flag_j-1) +1:m*flag_j]);
Junzhi_ij (1,flag_j) =mean (YUANSU_IJ);
Biaozhuencha_ij (1,flag_j) =sqrt (Mean (Yuansu_ij-junzhi_ij (1,flag_j)). ^2);
Leijilicha_ij=cumsum (Yuansu_ij-junzhi_ij (1,flag_j));
Jicha_ij (1,flag_j) =max (Leijilicha_ij)-min (LEIJILICHA_IJ);
End
RS (1,flag_i) =mean (JICHA_IJ./BIAOZHUENCHA_IJ);
End

Percent-fitting piecewise Xulie and Rs sequences to find the Hurst exponent
Temp1=find (isNaN (RS)); RS (TEMP1) =[];xulie (TEMP1) =[];
Line_h=polyfit (log10 (Xulie), log10 (RS), 1);

Percent drawing
% subplot (1,2,1);p lot (x);
% subplot (1,2,2);
% Plot (log10 (N./xulie (1:len_xulie)), log10 (RS (1:len_xulie)), ' Ro ');
% Plot (log10 (N./xulie (1:len_xulie)), Polyval (LINE_H,LOG10 (N./xulie)), ' 1:len_xulie ');
% title ([' Fitted linear slope ', Num2str (Line_h (1))]);
% Log_n_rs=[log10 (N./xulie (1:len_xulie); log10 (RS (1:len_xulie))];
%

The relationship between Percent Hurst index and correlation
% (1) When 0.5% (2) when h=0.5, stating that the time series is irrelevant, is an independent stochastic process, that is, the current state does not affect the future state.
% (3) when 0

There are three forms of the Hurst Index:
% 1. If h=0.5, indicates that the time series can be described by random walk;
% 2. If 0.5% 3. If 0≤h<0.5, it indicates that the pink noise (anti-persistent) is the mean-value recovery process.
In other words, as long as the h≠0.5, you can use a biased Brownian motion (fractal Brownian motion) to describe the time series data.

Percent Polyfit (Fit) and Polyval (interpolation) application examples
% x = (0:0.1:2.5) ';
% y = Erf (x);
% P = polyfit (x,y,6);
% Y1=polyval (p,x);
% subplot (1,3,1);p lot (x, y, '-b* ');
% subplot (1,3,2);p lot (x,y1, '-ro ');
% subplot (1,3,3);p lot (x, y, '-b* '), hold On;plot (x,y1, '-ro ');

Input of Percent-N
% 2.^[2:15] '
% 4
% 8
% 16
% 32
% 64
% 128
% 256
% 512
% 1024
% 2048
% 4096
% 8192
% 16384
% 32768
End

Continuous research on the trend of stock index (Hurst index)