Effect of trends on detrended fluctuation analysis.
TLDR
It is shown how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.Abstract:
scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ‘‘apparent’’ scaling of the trend. We study how the characteristics of these crossovers depend on ~i! the slope of the linear trend; ~ii! the amplitude and period of the periodic trend; ~iii! the amplitude and power of the power-law trend, and ~iv! the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws—i.e., long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. In addition, we show how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.read more
Citations
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Detrending fluctuation analysis based on high-pass filtering
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Dynamics of electricity market correlations
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Generalized (m, k)-Zipf Law for Fractional Brownian Motion-Like Time Series with or Without Effect of an Additional Linear Trend
Ph. Bronlet,Marcel Ausloos +1 more
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Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations
Pedro Carpena,Manuel Gómez-Extremera,Concepción Carretero-Campos,Pedro Bernaola-Galván,Ana V. Coronado +4 more
TL;DR: Analytical and numerical evidence is presented 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.
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