Next Article in Journal
Projection to Mixture Families and Rate-Distortion Bounds with Power Distortion Measures
Next Article in Special Issue
The Entropy of Words—Learnability and Expressivity across More than 1000 Languages
Previous Article in Journal / Special Issue
Self-Organized Patterns Induced by Neimark-Sacker, Flip and Turing Bifurcations in a Discrete Predator-Prey Model with Lesie-Gower Functional Response
Article Menu
Issue 6 (June) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(6), 261; doi:10.3390/e19060261

Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations

Departamento de Física Aplicada II, E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071 Málaga, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Gunnar Pruessner
Received: 10 May 2017 / Revised: 31 May 2017 / Accepted: 2 June 2017 / Published: 7 June 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
View Full-Text   |   Download PDF [385 KB, uploaded 8 June 2017]   |  

Abstract

Fluctuation Analysis (FA) and specially Detrended Fluctuation Analysis (DFA) are techniques commonly used to quantify correlations and scaling properties of complex time series such as the observable outputs of great variety of dynamical systems, from Economics to Physiology. Often, such correlated time series are analyzed using the magnitude and sign decomposition, i.e., by using FA or DFA to study separately the sign and the magnitude series obtained from the original signal. This approach allows for distinguishing between systems with the same linear correlations but different dynamical properties. However, here we present analytical and numerical evidence showing that FA and DFA can lead to spurious results when applied to sign and magnitude series obtained from power-law correlated time series of fractional Gaussian noise (fGn) type. Specifically, we show that: (i) the autocorrelation functions of the sign and magnitude series obtained from fGns are always power-laws; However, (ii) when the sign series presents power-law anticorrelations, FA and DFA wrongly interpret the sign series as purely uncorrelated; Similarly, (iii) when analyzing power-law correlated magnitude (or volatility) series, FA and DFA fail to retrieve the real scaling properties, and identify the magnitude series as purely uncorrelated noise; Finally, (iv) using the relationship between FA and DFA and the autocorrelation function of the time series, we explain analytically the reason for the FA and DFA spurious results, which turns out to be an intrinsic property of both techniques when applied to sign and magnitude series. View Full-Text
Keywords: complex time series; power-law correlations; detrended fluctuation analysis; magnitude and sign decomposition complex time series; power-law correlations; detrended fluctuation analysis; magnitude and sign decomposition
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Carpena, P.; Gómez-Extremera, M.; Carretero-Campos, C.; Bernaola-Galván, P.; Coronado, A.V. Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations. Entropy 2017, 19, 261.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top