Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses
arXiv:2004.03319 · doi:10.1007/s11071-020-05581-y
Abstract
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of Hölder exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality.
To appear in Nonlinear Dynamics
References in corpus (25)
- Multifractal detrended fluctuation analysis of nonstationary time series
- Surrogate time series
- Multifractality in Human Heartbeat Dynamics
- Effect of Trends on Detrended Fluctuation Analysis
- Detrending moving average algorithm for multifractals
- Multifractal analysis of financial markets
- Wavelet versus Detrended Fluctuation Analysis of multifractal structures
- Multifractal methodology
- Quantitative features of multifractal subtleties in time series
- Detecting and interpreting distortions in hierarchical organization of complex time series
- Multifractality in the stock market: price increments versus waiting times
- Components of multifractality in high-frequency stock returns
- Multi-scaling properties of truncated Levy flights
- Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series
- Effect of detrending on multifractal characteristics
- Multifractal nature of stock exchange prices
- Long-range correlation and multifractality in Bach's Inventions pitches
- Fractal and Multifractal Properties of Electrographic Recordings of Human Brain Activity: Toward Its Use as a Signal Feature for Machine Learning in Clinical Applications
- Dynamical variety of shapes in financial multifractality
- Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant
- Multifractal analysis of DNA walks and trails
- Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis
- Boundary criticality and multifractality at the 2D spin quantum Hall transition
- Uncovering latent singularities from multifractal scaling laws in mixed asymptotic regime. Application to turbulence
- Right-side-stretched multifractal spectra indicate small-worldness in networks
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- Corrupted bifractal features in finite uncorrelated power-law distributed data