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

Marc Höll, Holger Kantz

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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.

Original languageEnglish
Article number126
JournalEuropean Physical Journal B
Volume88
Issue number5
DOIs
StatePublished - 15 May 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

Keywords

  • Statistical and Nonlinear Physics

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