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Effect of Trends on Detrended Fluctuation Analysis | | Kun Hu
; Plamen Ch. Ivanov
; Zhi Chen
; Pedro Carpena
; H. Eugene Stanley
; | | Date: |
8 Mar 2001 | | Journal: | Physical Review E, vol. 64, 011114, 2001 | | Subject: | Data Analysis, Statistics and Probability; Statistical Mechanics; Biological Physics | physics.data-an cond-mat.stat-mech physics.bio-ph | | Affiliation: | 1 and 2), Zhi Chen , Pedro Carpena , H. Eugene Stanley ( Boston University, Harvard Medical School, Universidad de Malaga | | Abstract: | 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 superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. | | Source: | arXiv, physics/0103018 | | Other source: | [GID 1076102] pmid11461232 | | Services: | Forum | Review | PDF | Favorites | |
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