Eur. Phys. J. B (2015) 88: 126
https://doi.org/10.1140/epjb/e2015-60143-1

Regular Article

The fluctuation function of the detrended fluctuation analysis – investigation on the AR(1) process

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

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

Received: 24 February 2015
Received in final form: 9 April 2015
Published online: 18 May 2015

Abstract

We derive an analytical expression for the fluctuation function of the first order autoregressive process AR(1) by means of the detrended fluctuation analysis (DFA). This process is short-range correlated and therefore the fluctuation exponent should be α = 1/2. However, the fluctuation function exhibits a crossover between a region with α > 1/2 and the expected 1/2. We calculate the crossover point and compare it with the characteristic correlation time of the process. We conclude that DFA is data consuming and requires one to two orders of magnitude more data than the estimation of the autocorrelation function.