Tempting long-memory - on the interpretation of DFA results

Loading...
Thumbnail Image
Date
2004
Volume
11
Issue
4
Journal
Nonlinear Processes in Geophysics
Series Titel
Book Title
Publisher
Göttingen : Copernicus GmbH
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.

Description
Keywords
Citation
Maraun, D., Rust, H. W., & Timmer, J. (2004). Tempting long-memory - on the interpretation of DFA results (Göttingen : Copernicus GmbH). Göttingen : Copernicus GmbH. https://doi.org//10.5194/npg-11-495-2004
License
CC BY-NC-SA 2.5 Unported