Trend-adjusting fluctuation analysis
The detrended fluctuation analysis (engl. Detrended fluctuation analysis DFA) is a mathematical tool for analysis of time series , series of measurements and any equidistant sequences. It is used for quantification of long-term correlations and help u. a. in describing and predicting the behavior of complex systems .
The examined series usually consist of a random and a systematic component (non- stationary at least in the first moment ), which cannot be easily separated. Assuming an additive composition, the autocorrelations can be characterized on large time scales using the DFA, whereby the systematic changes ( trends ) on all scales are faded out (trend adjustment). This is not possible with the numerically calculated autocorrelation function, as it presupposes stationarity (freedom from trends) on the one hand and fluctuates strongly on large scales on the other .
The DFA will u. a. used in the analysis of biological data, for example in the detection of coding regions in gene sequences of DNA . In addition, it is also used to investigate meteorological and hydrological data, for example to investigate the long-term dependencies of temperatures and amounts of precipitation .
literature
- Peng, CK et al .: Mosaic organization of DNA nucleotides , 1994, Phys Rev E, 49 (2) 1685-1689, doi : 10.1103 / PhysRevE.49.1685 .
- Kantelhardt, JW et al .: Detecting long-range correlations with detrended fluctuation analysis , 2001, Phys A, 295 (3–4) 441–454, doi : 10.1016 / S0378-4371 (01) 00144-3 , arxiv : cond- mat / 0102214 .
- Bunde, A. and Kantelhardt, JW: Long-term correlations in nature: of climate, genetic material and heart rhythm , 2001, Phys Blätter, 57 (5) 49–54, doi : 10.1002 / phbl.20010570520 .