RSSTATISTIC Procedure

@RSStatistic computes the R/S (rescaled range) statistic for a single sample. It can either compute the classical R/S statistic from Mandelbrot and Wallis(1969), or Lo(1991)'s modified version. This is used in analyzing long-term memory of a process.

@RSStatistic( options ) x start end

Parameters

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

Options

CLASSICAL/[NOCLASSICAL]

If CLASSICAL, it computes the classical form (range divided by sample standard deviation). If NOCLASSICAL (the default) it computes Lo's modified form, where the scale is the square root of the long-run variance. Lo's statistic is also divided by the square root of the number of observations.

LAGS=Bartlett window width for computing Lo's statistic [sqrt(observations)]

Notes

Because the R/S statistic is usually computed for many different samples, this procedure doesn't display any output. Instead, use it to do the number-crunching, and retrieve the result with %CDSTAT.

Variables Defined

%CDSTAT

Calculated R/S statistic

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

set vq 1 101 = 0.0

set xq 1 101 = t+1

source rsstatistic.src

do q=0,100

@RSStatistic(lags=q) ew

compute vq(q+1)=%cdstat

end do q

scatter(header="Fig 2b. V(q) for the EW series on a log-log scale",$

style=line,vlabel="V(q)",hlabel="q",vlog=2,hlog=4)

# xq vq