Detecting long-range correlations with detrended fluctuation analysis

We examine the detrended fluctuation analysis (DFA), which is a well-establ ished method for the detection of long-range correlations in time series. W e show that deviations from scaling which appear at small time scales becom e stronger in higher orders of DFA, and suggest a modified DFA method to re move them. The improvement is necessary especially for short records that a re affected by non-stationarities, Furthermore, we describe how crossovers in the correlation behavior can be detected reliably and determined quantit atively and show how several types of trends in the data affect the differe nt orders of DFA. (C) 2001 Elsevier Science B.V. All rights reserved.