HURST Procedure

This calculates the Hurst exponent for a series, which measures long-run dependence. This will

•Plot the LOG(R/S) vs. LOG(# of OBS), (base 10 logs, not natural logs). Only if you use GRAPH option

•Prompt you to select the range over which you want to run the regression of LOG(R/S) on CONSTANT and LOG(# of OBS) to get the Hurst exponent (coefficient on the LOG(# of obs.) series). (If you use NODIALOG, it will use a standard range).

•Do the regression, storing the calculated hurst exponent in a global real variable called %%HURST.

•Repeat the first plot, this time with a line representing the calculated Hurst exponent.

@HURST( options ) series start end

Parameters

series	series to analyze
start end	range of series to use. By default, the defined range of series.

Options

[GRAPH]/NOGRAPH

Controls graphing of LOG(R/S) vs. LOG(N)

HEADER=header for graph

[PRINT]/NOPRINT

Controls printing of the log-log regression

[DIALOG]/NODIALOG

Controls whether you are prompted for the range over which to run the log-log regression

Variables Defined

%%HURST

calculated Hurst exponent

Example

* Replication file for Willinger, Taqqu and Teverovsky(1999), "Stock

* Market Prices and Long-Range Dependence", Finance and Stochastics, vol

* 3 pp 1-13.

open data d-vwew.dat

data(format=free,org=columns) 1 6409 date vw ew

graph(header="Trace of the Equal-Weighted CRSP daily data")

# ew

@hurst(header="R/S Analysis of Equally-Weighted Returns") ew