Eur. Phys. J. B (2015) 88: 327
https://doi.org/10.1140/epjb/e2015-60721-1

Regular Article

The relationship between the detrendend fluctuation analysis and the autocorrelation function of a signal

Max Planck Institute for the Physics of Complex Physics, Nöthnitzer Str. 38, 01187 Dresden, Germany

^a e-mail: hoell@pks.mpg.de

Received: 4 September 2015
Received in final form: 22 October 2015
Published online: 9 December 2015

Abstract

We derive an analytical expression for the fluctuation function of the detrended fluctuation analysis and state the relationship with the autocorrelation function for stationary processes. With this result we can investigate the scaling of the fluctuation function for short-range and long-range correlated processes. Furthermore we show that short-range correlated processes always exhibit a crossover between regions of different scaling. We also extend our results to processes with additive trends and discuss the effect of measurement noise.