eprintid: 10081921
rev_number: 26
eprint_status: archive
userid: 608
dir: disk0/10/08/19/21
datestamp: 2019-10-28 19:39:34
lastmod: 2022-04-06 12:35:00
status_changed: 2019-10-28 19:39:34
type: working_paper
metadata_visibility: show
creators_name: Botcharova, M
creators_name: Farmer, SF
creators_name: Berthouze, L
title: A maximum likelihood based technique for validating detrended fluctuation analysis (ML-DFA)
ispublished: pub
divisions: UCL
divisions: B02
divisions: C07
divisions: D07
divisions: C09
divisions: D13
divisions: G26
note: This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
abstract: Detrended Fluctuation Analysis (DFA) is widely used to assess the presence of long-range temporal correlations in time series. Signals with long-range temporal correlations are typically defined as having a power law decay in their autocorrelation function. The output of DFA is an exponent, which is the slope obtained by linear regression of a log-log fluctuation plot against window size. However, if this fluctuation plot is not linear, then the underlying signal is not self-similar, and the exponent has no meaning. There is currently no method for assessing the linearity of a DFA fluctuation plot. Here we present such a technique, called ML-DFA. We scale the DFA fluctuation plot to construct a likelihood function for a set of alternative models including polynomial, root, exponential, logarithmic and spline functions. We use this likelihood function to determine the maximum likelihood and thus to calculate values of the Akaike and Bayesian information criteria, which identify the best fit model when the number of parameters involved is taken into account and over-fitting is penalised. This ensures that, of the models that fit well, the least complicated is selected as the best fit. We apply ML-DFA to synthetic data from FARIMA processes and sine curves with DFA fluctuation plots whose form has been analytically determined, and to experimentally collected neurophysiological data. ML-DFA assesses whether the hypothesis of a linear fluctuation plot should be rejected, and thus whether the exponent can be considered meaningful. We argue that ML-DFA is essential to obtaining trustworthy results from DFA.
date: 2013-06-21
publisher: arXiv.org
official_url: https://arxiv.org/abs/1306.5075
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
commissioning_body: Cornell University
verified: verified_manual
elements_id: 880150
lyricists_name: Berthouze, Luc
lyricists_name: Farmer, Simon
lyricists_id: LBERT20
lyricists_id: SFFAR49
actors_name: Farmer, Simon
actors_id: SFFAR49
actors_role: owner
full_text_status: public
place_of_pub: Ithaca (NY), USA
pages: 22
citation:        Botcharova, M;    Farmer, SF;    Berthouze, L;      (2013)    A maximum likelihood based technique for validating detrended fluctuation analysis (ML-DFA).                    arXiv.org: Ithaca (NY), USA.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10081921/1/1306.5075v1.pdf