Detrended fluctuation analysis

The Trendbereinigende fluctuation analysis (English Detrended fluctuation analysis DFA ) is a mathematical tool for the analysis of time series, measurements and any equidistant sequences. It is used to quantify the long-term correlation and helps, inter alia, in the description and predict the behavior of complex systems.

The investigated series consist in general of a random component and a systematic component ( nonstationarity at least the first moment ), which can not be separated easily. Assuming an additive composition can the characterize autocorrelations on long time scales by means of the DFA, the systematic changes (trends) are hidden on all scales ( detrending ). This is not possible as with the numerically calculated autocorrelation function, since the latter one hand, stationarity implies (trend freedom ) and on the other hand, fluctuates greatly on large scales.

DFA is, inter alia, in the analysis of biological data for use, for example for the detection of gene sequences in coding regions of the DNA. In addition, it is also used for the study of meteorological and hydrological data, such as for the study of long-term dependencies at temperatures and rainfall.