Articles | Volume 11, issue 4
Nonlin. Processes Geophys., 11, 495–503, 2004
https://doi.org/10.5194/npg-11-495-2004

Special issue: Nonlinear analysis of multivariate geoscientific data - advanced...

Nonlin. Processes Geophys., 11, 495–503, 2004
https://doi.org/10.5194/npg-11-495-2004

  10 Nov 2004

10 Nov 2004

Tempting long-memory - on the interpretation of DFA results

D. Maraun1, H. W. Rust2, and J. Timmer3 D. Maraun et al.
  • 1Department of Physics, Potsdam University, D-14415 Potsdam, Germany
  • 2Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, D-14412 Potsdam, Germany
  • 3Center for Data Analysis and Modeling, Albert-Ludwigs Universität, D-79104 Freiburg, Germany

Abstract. We study the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) and argue that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires the investigation of the local slopes. We account for the variability characteristic for stochastic processes by calculating empirical confidence regions. Comparing a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. We remark that scaling cannot be concluded from a straight line fit to the fluctuation function in a log-log representation. Furthermore, we show that a local slope larger than α=0.5 for large scales does not necessarily imply long-memory. We also demonstrate, that it is not valid to conclude from a finite scaling region of the fluctuation function to an equivalent scaling region of the autocorrelation function. Finally, we review DFA results for the Prague temperature data set and show that long-range correlations cannot not be concluded unambiguously.