Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 11 4 2004 10.5194/npg-11-495-2004 http://www.nonlin-processes-geophys.net/11/495/2004/ http://www.nonlin-processes-geophys.net/11/495/2004/npg-11-495-2004.html http://www.nonlin-processes-geophys.net/11/495/2004/npg-11-495-2004.pdf 495 503 2004-11-10 Tempting long-memory - on the interpretation of DFA results D. Maraun H. W. Rust J. Timmer Department of Physics, Potsdam University, D-14415 Potsdam, Germany Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, D-14412 Potsdam, Germany Center for Data Analysis and Modeling, Albert-Ludwigs Universität, D-79104 Freiburg, Germany 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.