NEW INSIGHTS INTO THE ESTIMATION OF SCALING EXPONENTS

Bruno Lashermes · Patrice Abry · Pierre Chainais

121 citations0/0 files storedInternational Journal of Wavelets Multiresolution and Information Processing

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Complex Systems and Time Series Analysis Theoretical and Computational Physics Statistical Mechanics and Entropy

Abstract

We study the statistical performance of multiresolution-based estimation procedures for the scaling exponents of multifractal processes. These estimators rely on the computation of multiresolution quantities such as wavelet, increment or aggregation coefficients. Estimates are obtained by linear fits performed in log of structure functions of order q versus log of scale plots. Using various and recent types of multiplicative cascades and a large variety of multifractal processes, we study and benchmark, by means of numerical simulations, the statistical performance of these estimation procedures. We show that they all undergo a systematic linearisation effect: for a range of orders q, the estimates account correctly for the scaling exponents; outside that range, the estimates significantly depart from the correct values and systematically behave as linear functions of q. The definition and characterisation of this effect are thoroughly studied. In contradiction with interpretations proposed in the literature, we provide numerical evidence leading to the conclusion that this linearisation effect is neither a finite size effect nor an infiniteness of moments effect, but that its origin should be related to the deep nature of the process itself. We comment on its importance and consequences for the practical analysis of the multifractal properties of empirical data.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 121 citations exist upstream.

References

1998Wavelet analysis of long-range-dependent traffic 2001Multifractal random walk 1999A Multifractal Walk down Wall Street 2002Log-Infinitely Divisible Multifractal Processes 2002Multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws

Cited by

2016Multifractal detrended fluctuation analysis: Practical applications to financial time series 2007Continuous cascade models for asset returns 2005On Non-Scale-Invariant Infinitely Divisible Cascades 2021Herding behavior during the Covid-19 pandemic: a comparison between Asian and European stock markets based on intraday multifractality 2022Correlations between the crude oil market and capital markets under the Russia–Ukraine conflict: A perspective of crude oil importing and exporting countries 2006Wavelet Leader based Multifractal Analysis 2021COVID-19, bitcoin market efficiency, herd behaviour 2023The dynamics of market efficiency of major cryptocurrencies

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.