Genuine multifractality in time series is due to temporal correlations

Area of Science:

• Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• Multifractality in time series analysis is often attributed to broad distribution tails or temporal correlations.
• The multifractal detrended fluctuation analysis (MFDFA) is a common method for quantifying multifractality.

Purpose of the Study:

• To investigate the origins of multifractality in time series.
• To differentiate the contributions of temporal correlations versus distribution tails to observed multifractality.

Main Methods:

• Mathematical formulation using multifractal detrended fluctuation analysis (MFDFA).
• Numerical simulations to illustrate and confirm theoretical findings.
• Analysis of both Gaussian and Lévy stable fluctuation regimes.

Main Results:

• Apparent multifractality in uncorrelated Gaussian time series diminishes with increasing series length.
• Genuine multifractality is demonstrated to stem exclusively from long-range temporal correlations.
• Broad distribution tails only widen the singularity spectrum in the presence of correlations.

Conclusions:

• The question of whether temporal correlations or broad distribution tails cause multifractality is ill-posed; correlations are essential.
• In uncorrelated series, only monofractal (Gaussian) or bifractal (Lévy stable) behaviors are observed.
• MFDFA reveals that multifractality is a signature of temporal correlations in time series data.