Modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti-persistent processes

Detrended fluctuation analysis (DFA) is a simple but very efficientmethod for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at different timescales. We propose to determine the local trends through empirical mode decomposition (EMD) and perform the detrending operation by removing the EMD-based local trends, which gives an EMDbasedDFAmethod. Similarly,we also propose amodifiedmultifractal DFA algorithm, called an EMD-based MFDFA. The performance of the EMD-based DFA and MFDFA methods is assessed with extensive numerical experiments based on fractional Brownian motion and multiplicative cascading process.We find that the EMD-basedDFAmethod performs better than the classic DFA method in the determination of the Hurst index when the time series is strongly anticorrelated and the EMD-based MFDFA method outperforms the traditional MFDFA method when the moment order q of the detrended fluctuations is positive. We apply the EMD-based MFDFA to the 1 min data of Shanghai Stock Exchange Composite index, and the presence of multifractality is confirmed. We also analyze the daily Austrian electricity prices and confirm its anti-persistence. © 2011 Elsevier B.V. All rights reserved.