Keylock, C.J. orcid.org/0000-0002-9517-9896 (2018) Gradual multifractal reconstruction of time-series: Formulation of the method and an application to the coupling between stock market indices and their Hölder exponents. Physica D: Nonlinear Phenomena, 368. pp. 1-9. ISSN 0167-2789
Abstract
A technique termed gradual multifractal reconstruction (GMR) is formulated. A continuum is defined from a signal that preserves the pointwise Hölder exponent (multifractal) structure of a signal but randomises the locations of the original data values with respect to this (ϕ=0), to the original signal itself(ϕ=1). We demonstrate that this continuum may be populated with synthetic time series by undertaking selective randomisation of wavelet phases using a dual-tree complex wavelet transform. That is, the ϕ=0 end of the continuum is realised using the recently proposed iterated, amplitude adjusted wavelet transform algorithm (Keylock, 2017) that fully randomises the wavelet phases. This is extended to the GMR formulation by selective phase randomisation depending on whether or not the wavelet coefficient amplitudes exceeds a threshold criterion. An econophysics application of the technique is presented. The relation between the normalised log-returns and their Hölder exponents for the daily returns of eight financial indices are compared. One particularly noticeable result is the change for the two American indices (NASDAQ 100 and S & P 500) from a non-significant to a strongly significant (as determined using GMR) cross-correlation between the returns and their Hölder exponents from before the 2008 crash to afterwards. This is also reflected in the skewness of the phase difference distributions, which exhibit a geographical structure, with Asian markets not exhibiting significant skewness in contrast to those from elsewhere globally.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2017 Elsevier. This is an author produced version of a paper subsequently published in Physica D: Nonlinear Phenomena. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Wavelets; Multifractal; Hölder exponent; Surrogate data; Econophysics |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/K007688/1 NATURAL ENVIRONMENT RESEARCH COUNCIL NE/F00415X/2 LEVERHULME TRUST (THE) NONE |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Jan 2018 14:34 |
Last Modified: | 28 Jul 2020 14:55 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.physd.2017.11.011 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:125982 |