Hurst exponents and delampertized fractional Brownian motions

Matthieu Garcin ()
Additional contact information
Matthieu Garcin: DVRC - De Vinci Research Center - DVHE - De Vinci Higher Education

Working Papers from HAL

Abstract: The inverse Lamperti transform of a fractional Brownian motion is a stationary process. We determine the empirical Hurst exponent of such a composite process with the help of a regression of the log absolute moments of its increments, at various scales, on the corresponding log scales. This perceived Hurst exponent underestimates the Hurst exponent of the underlying fractional Brownian motion. We thus encounter some time series having a perceived Hurst exponent lower than 1/2, but an underlying Hurst exponent higher than 1/2. This paves the way for short-and medium-term forecasting. Indeed, in such series, mean reversion predominates at high scales, whereas persistence is overriding at lower scales. We propose a way to characterize the Hurst horizon, namely a limit scale between these opposite behaviours. We show that the delampertized fractional Brownian motion, which mixes persistence and mean reversion, is relevant for financial time series, in particular for high-frequency foreign exchange rates. In our sample, the empirical Hurst horizon is always above 1 hour and 23 minutes.

Keywords: fractional Brownian motion; Hurst exponent; Lamperti transform; Ornstein-Uhlenbeck process; foreign exchange rates (search for similar items in EconPapers)
Date: 2018-11-12
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: View the original document on HAL open archive server: https://hal.science/hal-01919754v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-01919754v1/document (application/pdf)

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:hal:wpaper:hal-01919754

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().