The RATS Software Forum

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

Mandelbrot and Wallis(1969), "Computer Experiments with Fractional Gaussian Noise", Water Resources Res., vol 5, 228-267.
Lo(1991) "Long-term Memory in Stock Market Prices", Econometrica, vol 59, 1279-1313.

Detailed description

Dear Tom,

I was replicating the results of the paper : Willinger, Taqqu and Teverovsky(1999), "Stock Market Prices and Long-Range Dependence", Finance and Stochastics, vol 3 pp 1-13. The values of H turn out to be more or less the same given in the paper. I must appreciate your efforts.

I would like to get the values of AR and MA coefficients [(-0.16, -0.40)] mentioned by the authors on page number 10 of the paper. Could you please help me? On page number 11, first paragraph, author referred the value of H=0.58 for blocks of 20 which turns out to be 0.6557 if we run the programme. Since the variation is large, I think I should report it to you.

On the same page, the author refers the value of H=0.5 in the lase line of second paragraph. May I know how do I get it? Do we have to use the following programme?

boot(block=40,method=nooverlap) shuffle
set reshuffle = ew(shuffle(t))
@hurst(header="R/S Analysis of Block Shuffled Returns") reshuffle

If I run it, I get the value of H=0.64851 not 0.5?
Please reply,
With regards,
Prashant

prashantj wrote:Dear Tom,

I was replicating the results of the paper : Willinger, Taqqu and Teverovsky(1999), "Stock Market Prices and Long-Range Dependence", Finance and Stochastics, vol 3 pp 1-13. The values of H turn out to be more or less the same given in the paper. I must appreciate your efforts.

I would like to get the values of AR and MA coefficients [(-0.16, -0.40)] mentioned by the authors on page number 10 of the paper. Could you please help me?

I posted an updated version of this at http://www.estima.com/forum/viewtopic.php?f=8&t=2059 which uses better guess values for the estimation of the ARFIMA.

prashantj wrote: On page number 11, first paragraph, author referred the value of H=0.58 for blocks of 20 which turns out to be 0.6557 if we run the programme. Since the variation is large, I think I should report it to you.

The calculation of the Hurst exponent depends upon the range over which the regression of the log(R/S) to log(N) is done. Different subranges makes different estimates.

prashantj wrote: On the same page, the author refers the value of H=0.5 in the lase line of second paragraph. May I know how do I get it? Do we have to use the following programme?

boot(block=40,method=nooverlap) shuffle
set reshuffle = ew(shuffle(t))
@hurst(header="R/S Analysis of Block Shuffled Returns") reshuffle

If I run it, I get the value of H=0.64851 not 0.5?

.5 is the value for a process without long memory. Those are bootstrapped values, so there is no way to reproduce a value that they show in the paper.