On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data

Dariusz Grech and Zygmunt Mazur

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 10, 2384-2397

Abstract: We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series length L and the correlation coefficient of the linear regression R2 at various confidence levels. Next, a similar analysis for artificial short series of data with long-term memory is performed. In both cases the scaling range λ is found to change linearly—both with L and R2. We show how this dependence can be generalized to a simple unified model describing the relation λ=λ(L,R2,H) where H (1/2≤H≤1) stands for the Hurst exponent of the long range autocorrelated signal. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where a huge number of short time series has to be analyzed at the same time, without possibility of checking the scaling range in each of them separately.

Keywords: Scaling range; Scaling laws; Detrended fluctuation analysis; Hurst exponent; Time series; Numerical analysis; Long-term memory; Econophysics; Complex systems (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (19)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:10:p:2384-2397

DOI: 10.1016/j.physa.2013.01.049

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