Direct determination approach for the multifractal detrending moving average analysis

Hai-Chuan Xu, Gao-Feng Gu, and Wei-Xing Zhou
Phys. Rev. E 96, 052201 – Published 3 November 2017

Abstract

In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent τ(q) is related to the partition function and the multifractal spectrum f(α) can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional p-model, the two-dimensional p-model, and the fractional Brownian motions. We find that both approaches have comparable performances to unveil the fractal and multifractal nature. In other words, without loss of accuracy, the multifractal spectrum f(α) can be directly determined using the new approach with less computation cost. We also apply the new MF-DMA approach to the volatility time series of stock prices and confirm the presence of multifractality.

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  • Received 14 June 2017

DOI:https://doi.org/10.1103/PhysRevE.96.052201

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Nonlinear DynamicsInterdisciplinary PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Hai-Chuan Xu1,2, Gao-Feng Gu1,2, and Wei-Xing Zhou1,2,3,*

  • 1Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China
  • 2Department of Finance, East China University of Science and Technology, Shanghai 200237, China
  • 3School of Science, East China University of Science and Technology, Shanghai 200237, China

  • *wxzhou@ecust.edu.cn

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Issue

Vol. 96, Iss. 5 — November 2017

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