A note on geometric method-based procedures to calculate the Hurst exponent

J.E. Trinidad Segovia, M. Fernández-Martínez and M.A. Sánchez-Granero
Authors registered in the RePEc Author Service: Juan Evangelista Trinidad-Segovia ()

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 6, 2209-2214

Abstract: Geometric method-based procedures, which we will call GM algorithms hereafter, were introduced in M.A. Sánchez-Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543–5551, to calculate the Hurst exponent of a time series. The authors proved that GM algorithms, based on a geometrical approach, are more accurate than classical algorithms, especially with short length time series. The main contribution of this paper is to provide a mathematical background for the validity of these two algorithms to calculate the Hurst exponent H of random processes with stationary and self-affine increments. In particular, we show that these procedures are valid not only for exploring long memory in classical processes such as (fractional) Brownian motions, but also for estimating the Hurst exponent of (fractional) Lévy stable motions.

Keywords: Hurst exponent; Financial market; Long memory; GM algorithms; Fractal structure; Generalized fractal space (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:6:p:2209-2214

DOI: 10.1016/j.physa.2011.11.044

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