Related Experiment Video
Updated: Oct 12, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
Published on: June 27, 2013
Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set
Maria C Mariani1, William Kubin2, Peter K Asante2
1Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79902, USA.
Abstract:
In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.
Related Concept Videos
Basic Discrete Time Signals
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
Exponential Fourier series
Euler's identity...
Exponential and Sinusoidal Signals
Continuous -time Fourier Transform
Convergence of Fourier Series
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Basic Continuous Time Signals
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...

