Corrupted bifractal features in finite uncorrelated power-law distributed data

Abstract

Multifractal Detrended Fluctuation Analysis stands out as one of the most reliable methods for unveiling multifractal properties, specially when real-world time series are under analysis. However, little is known about how several aspects, like artefacts during the data acquisition process, affect its results. In this work we have numerically investigated the performance of Multifractal Detrended Fluctuation Analysis applied to synthetic finite uncorrelated data following a power-law distribution in the presence of additive noise, and periodic and randomly-placed outliers. We have found that, on one hand, spurious multifractality is observed as a result of data finiteness, while additive noise leads to an underestimation of the exponents $h_q$ for $q<0$ even for low noise levels. On the other hand, additive periodic and randomly-located outliers result in a corrupted inverse multifractality around $q=0$. Moreover, the presence of randomly-placed outliers corrupts the entire multifractal spectrum, in a way proportional to their density. As an application, the multifractal properties of the time intervals between successive aircraft landings at three major European airports are investigated.

17 pages, 11 figures, 2 tables

References in corpus (4)

• Multifractal detrended cross-correlation analysis for two nonstationary signals
• Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series
• Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses
• Computational approach to multifractal music

Cited by in corpus (2)

• Genuine multifractality in time series is due to temporal correlations
• Quantifying deviations from Gaussianity with application to flight delays distributions