Detrended fluctuation analysis in higher dimensions

by Keqiang Dong and Pengjian Shang.

Abstract: One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MF-DFA) are widely employed in detecting of long-range correlations of a time series owing to the simplicity and accuracy in implementation. Here we generalize the one-dimensional DFA and MF-DFA to two-dimensional versions. In this paper we relate two-dimensional scaling exponent to the one-dimensional correlation exponent, and prove that a linear relation between them is present. Furthermore, we illustrate the two-dimensional DFA method by synthetic two-dimensional time series and traffic data.

Key Words: Detrended fluctuation analysis; Traffic time series; Long-range correlation; Fourier transform method; multifractal time series Authors:

Keqiang Dong,
Pengjian Shang,

Editor: Youssef, Ahmed H,

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