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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)
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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

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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).

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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.

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