Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations
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...
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MDPI AG
2017-06-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/19/6/261 |
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| author | Pedro Carpena Manuel Gómez-Extremera Concepción Carretero-Campos Pedro Bernaola-Galván Ana V. Coronado |
| author_facet | Pedro Carpena Manuel Gómez-Extremera Concepción Carretero-Campos Pedro Bernaola-Galván Ana V. Coronado |
| author_sort | Pedro Carpena |
| collection | DOAJ |
| description | 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. |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:33:22Z |
| publishDate | 2017-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d54e1b482f0a4b1abd7af3a412b13cf42022-12-22T03:59:18ZengMDPI AGEntropy1099-43002017-06-0119626110.3390/e19060261e19060261Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign CorrelationsPedro Carpena0Manuel Gómez-Extremera1Concepción Carretero-Campos2Pedro Bernaola-Galván3Ana V. Coronado4Departamento de Física Aplicada II, E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071 Málaga, SpainDepartamento de Física Aplicada II, E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071 Málaga, SpainDepartamento de Física Aplicada II, E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071 Málaga, SpainDepartamento de Física Aplicada II, E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071 Málaga, SpainDepartamento de Física Aplicada II, E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071 Málaga, SpainFluctuation 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.http://www.mdpi.com/1099-4300/19/6/261complex time seriespower-law correlationsdetrended fluctuation analysismagnitude and sign decomposition |
| spellingShingle | Pedro Carpena Manuel Gómez-Extremera Concepción Carretero-Campos Pedro Bernaola-Galván Ana V. Coronado Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations Entropy complex time series power-law correlations detrended fluctuation analysis magnitude and sign decomposition |
| title | Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations |
| title_full | Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations |
| title_fullStr | Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations |
| title_full_unstemmed | Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations |
| title_short | Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations |
| title_sort | spurious results of fluctuation analysis techniques in magnitude and sign correlations |
| topic | complex time series power-law correlations detrended fluctuation analysis magnitude and sign decomposition |
| url | http://www.mdpi.com/1099-4300/19/6/261 |
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