Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: times
See also: fracbrown lo kpss

Macro: hurst
Description: estimates the Hurst coefficent of a process using the R/S statistics

Reference(s):

Usage: (ra,b,q)=hurst(x,k)
Input:
x n x 1 vector, observations of the process
k scalar, maximal number of intervals for the R/S statistic
Output:
ra (k-2) x 3 matrix, ra[,1] = (1, ... ,1)', ra[,2] = log(n/3, n/4, ... ,n/k)', ra[,3] = log(RS)
b 2 x 1 vector, b[1] = intercept of the R/S-line, b[2] = slope of R/S line, b solves the regression problem ra[,3] = b[1] + b[2]*ra[,2]
q scalar, residual varince of the regression problem

Note:

Example:
randomize(23)
func("hurst")		// load macro
x=cumsum(normal(500)) 	// simualte a brown. Motion (H = 0.5)
h=hurst(x,50)		
h.b[2]			// estimated H
Result:
Contents of _tmp
[1,]  0.54921 

Library: times
See also: fracbrown lo kpss

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Author: W. Härdle, T. Kleinow
(C) MD*TECH Method and Data Technologies, 28.6.1999