# A Monte Carlo simulation to the performance of the R/S and V/S methods—Statistical revisit and real world application

*Ling-Yun He* and
*Wen-Bin Qian*

*Physica A: Statistical Mechanics and its Applications*, 2012, vol. 391, issue 14, 3770-3782

**Abstract:**
A correct or precise estimation of the Hurst exponent is one of the fundamentally important problems in the financial economics literature. There are three widely used tools to estimate the Hurst exponent, the canonical rescaled range (R/S), the variance rescaled statistic (V/S) and the Modified rescaled range (Modified R/S). To clarify their performance, we compare them by Monte Carlo simulations; we generate many time-series of a fractal Brownian motion, of a Weierstrass–Mandelbrot cosine fractal function and of a fractionally integrated process, whose theoretical Hurst exponents are known, to compare the Hurst exponents estimated by the three methods. To better understand their pragmatic performance, we further apply all of these methods empirically in real-world applications. Our results imply it is not appropriate to conclude simply which method is better as V/S performs better when the analyzed market is anti-persistent while R/S seems to be a reliable tool used in persistent market.

**Keywords:** Monte Carlo simulations; Hurst exponent; R/S; V/S; Modified R/S; Fractal Brownian motion; Weierstrass function; Fractionally integrated process (search for similar items in EconPapers)

**Date:** 2012

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (13) Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0378437112001756

Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:14:p:3770-3782

**DOI:** 10.1016/j.physa.2012.02.028

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by *K. A. Dawson*, *J. O. Indekeu*, *H.E. Stanley* and *C. Tsallis*

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier

Bibliographic data for series maintained by Catherine Liu ().