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

 Quantlet: hurst Description: estimates the Hurst coefficient of a stochastic process using the R/S statistic.

Reference(s):
Beran, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, London. Hall, P., Härdle, W., Kleinow, T. and Schmidt, P. (2000). Semiparametric Bootstrap Approach to Hypothesis Tests And Confidence Intervals For The Hurst Coefficient. Statistical Inference for Stochastic Processes, Vol. 3.

 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]. The estimator for the Hurst coefficient is b[2]. q scalar, variance of the residuals of the regression problem

Note:
To compute RS (see output parameter ra), (1, ... , n) is divided into k subintervals and the rescaled range is computed. See the references for a detailed description.

Example:
```library("times")	// load library times
randomize(23)
x=cumsum(normal(500)) 	// simulate a Brownian motion(H = 0.5)
h=hurst(x,50)
h.b[2]			// estimate H

```
Result:
```Contents of _tmp
[1,]  0.54921
```

Author: W. Härdle, T. Kleinow, 20010503 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006