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

Abstract

We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long 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 length $L$ of time series and regression line coefficient $R^2$ at various confidence levels. Next, an analysis of artificial short series with long memory is performed. In both cases the scaling range $\lambda$ is found to change linearly -- both with $L$ and $R^2$. We show how this dependence can be generalized to a simple unified model describing the relation $\lambda =\lambda (L,R^2,H)$ where $H$ ($1/2\le H\le 1$) stands for the Hurst exponent of long range autocorrelated data. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where enormous number of short time series has to be examined at once, without possibility for preliminary check of the scaling range of each series separately.

27 pages, 17 figures

References in corpus (11)

• Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series
• Multifractal detrended cross-correlation analysis for two nonstationary signals
• Cross-correlations between volume change and price change
• Multifractal detrending moving average cross-correlation analysis
• Comparison of detrending methods for fluctuation analysis
• Effect of nonlinear filters on detrended fluctuation analysis
• Detrended fluctuation analysis for fractals and multifractals in higher dimensions
• Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series
• Finite sample properties of power-law cross-correlations estimators
• Blocks adjustment -- reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation
• On the scaling range of power-laws originated from fluctuation analysis

Cited by in corpus (11)

• Multifractal analysis of financial markets
• Direct determination approach for the multifractal detrending moving average analysis
• Turbulence-induced persistence in laser beam wandering
• Finite sample properties of power-law cross-correlations estimators
• Power-law cross-correlations estimation under heavy tails
• Linear and nonlinear correlations in order aggressiveness of Chinese stocks
• Robust linear regression with broad distributions of errors
• Persistence of temperature and precipitation: from local to global anomalies
• Scaling analyses based on wavelet transforms for the Talbot effect
• On the scaling range of power-laws originated from fluctuation analysis
• Model selection for identifying power-law scaling