Corrupted bifractal features in finite uncorrelated power-law distributed data

TL;DR

This paper investigates how data artifacts like noise and outliers affect the accuracy of Multifractal Detrended Fluctuation Analysis when applied to finite power-law distributed data, revealing significant distortions in multifractal spectra.

Contribution

It provides a numerical analysis of how additive noise and outliers distort multifractal analysis results on synthetic data, highlighting limitations of the method under data corruption.

Findings

Spurious multifractality arises from data finiteness.

Additive noise underestimates $h_q$ for $q<0$.

Outliers corrupt the multifractal spectrum proportionally to their density.

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.