如何生成具有指定範圍並與實際價格相關的隨機價格序列？

我想生成一個模擬價格系列。我希望它在一定範圍內，並與原始價格系列具有明確的相關性。

如果我選擇石油，我想要盡可能多的時間序列，它們在相關性方面具有一些相似的特徵，但並不精確。我不希望數據在與歷史路徑完全不同的路徑上徘徊。它不一定是協整的，相關就足夠了。我也希望這些堅持原來的價格範圍。系列應該是隨機的，例如每個新的實現都應該採用不同的路徑。

除了我對上面 Samik R 的回答的評論之外，這裡是我的部落格文章的連結，其中我嘗試重新創建連結到所述答案的方法。

根據 Tal Fishman 的評論進行編輯以包含更多資訊

八度 .oct 功能碼

#include <octave/oct.h>
#include <octave/dColVector.h>
#include <octave/CNDArray.h>
#include "MersenneTwister.h"

DEFUN_DLD (permute_vector, args, , "Input is a vector that is to be permuted once")
{
octave_value_list retval;

int nargin = args.length () ;
int vec_length = args(0).length () ;

// check the input arguments
   if ( nargin > 1 )
   {
   error ("Invalid arguments. Input is a vector that is to be permuted once") ;
   return retval ;
   }

   if (vec_length < 2 )
   {
   error ("Invalid arguments. Input is a vector that is to be permuted once") ;
   return retval ;
   }

   if (error_state)
   {
   error ("Invalid arguments. Input is a vector that is to be permuted once") ;
   return retval ;
   }
// end of input checking

ComplexNDArray input_vector = args(0).complex_array_value () ;
ComplexNDArray output_vector = args(0).complex_array_value () ;
int k1;
int k2;

MTRand mtrand1; // Declare the Mersenne Twister Class - will seed from system time

      k1 = vec_length - 1; // initialise prior to shuffling the vector

      while (k1 > 0) // While at least 2 left to shuffle
        {          
        k2 = mtrand1.randInt( k1 ); // Pick an int from 0 through k1 

          if (k2 > k1) // check if random vector index no. k2 is > than max vector    index - should never happen 
             {
             k2 = k1 - 1; // But this is cheap insurance against disaster if it does happen
             }

        output_vector(k1) = input_vector(k2) ; // allocate random pick k2 from input_vector to the k1 vector index of output_vector
        input_vector(k2) = input_vector(k1) ; // replace random pick k2 content of input_vector with content k1 of input_vector
        k1 = k1 - 1; // count down 
        } // Shuffling is complete when this while loop exits

retval(0) = output_vector ; 

return retval; // Return the output to Octave
} 

八度腳本程式碼

clear all

contract = input( "Enter contract symbol e.g. sp: ","s") ;
data = load("-ascii",contract) ;
n = rows(data)
index_begin = input( "Enter index_begin: ") ;
index_end = input( "Enter index_end, value not greater than n: ") ;

close = data(index_begin:index_end,7) ;

% detrend the close vector prior to applying the fft
slope = ( close(end) - close(1) ) / ( length(close) - 1 ) ;
v1 = (0:1:length(close)-1)' ;
detrended_close = close .- ( v1 .* slope ) ;
close_index_begin = close(1)
detrended_close_index_begin = detrended_close(1)
detrended_close_index_end = detrended_close(end)

% create zero padded vector for fft
L2 = 2^nextpow2( length(close) ) ; half_L2 = L2/2 ;
y2 = zeros( 1,L2 ) ; y2( 1:length(close) ) = detrended_close ;

% apply the fft
transform = fft( y2 ) ;

% permute the first half of the transform vector in "chunks" of 10
max_ii_value = floor( half_L2 / 10 ) ;
for ii = 1:max_ii_value
transform( (ii*10):(ii*10)+9 ) = permute_vector( transform( (ii*10):(ii*10)+9 ) ) ;
endfor

% take the inverse fft
ifft_vec = real( ifft( transform ) ) ;

% retrend the ifft_permuted_vec
retrended_ifft_vec = ifft_vec( 1:length(close) )' .+ ( v1 .* slope ) ;

% statistics
correl = corrcoef (close, retrended_ifft_vec)
spear = spearman (close, retrended_ifft_vec)
tau = kendall (close, retrended_ifft_vec)

plot( close,'b',retrended_ifft_vec,'r' ) ; legend( 'close','permute' ) ; 

更多資訊和圖表在我的部落格文章中。

引用自：https://quant.stackexchange.com/questions/2453