Effect of trends on detrended fluctuation analysis.

By K. Hu, Plamen Ch. Ivanov, Z. Chen, P. Carpena, H. University, H. School, U. Málaga. Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

1,241 citations recorded by the source corpus.

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends--linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the 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.

Subfields: Computer Networks and Communications, Condensed Matter Physics, Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/d175ec6efeacf3b3ad757c2c54badf8cc0d59da9

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Citations in the corpus

Tempting long-memory - on the interpretation of DFA results (2004, background): “The ability of DFA to estimateα from realizations of long-memory processes corrupted by different instationarities like trends, spikes, harmonics and gaps has been studied byHu et al.(2001), Chen et al.(2002) and Kantelhardt et al.(2001).”
Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection (2007, methodology): “Detrended fluctuation analysis is one straightforward technique for characterising the self-similarity of the graph of a signal from a stochastic process [54].”
Rescaled Range Analysis and Detrended Fluctuation Analysis: Finite Sample Properties and Confidence Intervals (2010, methodology): “The procedure is then labeled as DFA-0, DFA-1 and DFA-2 according to an order of the filtering trend (Hu et al. 2001).”
Autocorrelation and cross-correlation in time series of homicide and attempted homicide (2014, neutral): “[73].”
p-exponent and p-leaders, Part II: Multifractal Analysis. Relations to Detrended Fluctuation Analysis (2015, methodology): “In the MFDFA method, increasing NP also brings some form of robustness to additive noise, however, this far more depends on the nature of the trend [66, 67, 68, 69] (see also the numerical illustrations in Section 5.”
Multi-scaling in finance (2007, background): “…1997, Viswanathan et al. 1997, Ausloos et al. 1999, Janosi et al. 1999, Liu et al. 1999, Raberto et al. 1999, Stanley et al. 1999, Ausloos 2000, Hu et al. 2001, Chen et al. 2002, Ivanova and Ausloos 2002, Costa and Vasconcelos 2003) and its generalization (Kantelhardt et al. 2002, Matia et al.…”
Long‐range persistence in global Aerosol Index dynamics (2006, methodology): “The main aim of this paper was to search efficiently for time scaling in the AI time series, by using a data analysis technique that would not be affected by the nonstationarity of the data (Koscielny-Bunde et al. 1998, Hu et al. 2001, Kantelhardt et al. 2002).”