Randomized multifractal detrended fluctuation analysis of long time series

Area of Science:

• Complex Systems Analysis
• Bioinformatics
• Time Series Analysis

Background:

• Investigating multifractal properties of long time series is crucial for understanding complex systems.
• Existing methods like multifractal temporally weighted detrended fluctuation analysis (MFTWDFA) can be computationally intensive.

Purpose of the Study:

• To introduce a novel, time-efficient randomized method for multifractal analysis of long time series.
• To evaluate the performance and accuracy of the new method against established techniques.

Main Methods:

• Development of randomized multifractal temporally weighted detrended fluctuation analysis (RMFTWDFA) by incorporating randomization into interval division for local trend identification.
• Application of both RMFTWDFA and MFTWDFA to synthetic time series and large-scale prokaryote genomic sequences.

Main Results:

• RMFTWDFA demonstrates statistically comparable accuracy in estimating multifractal exponents (h(q)) compared to MFTWDFA.
• RMFTWDFA significantly reduces computation time by over tenfold for long sequences.
• Analysis of genomic sequences reveals fractal characteristics and supports phylogenetic relationship studies.

Conclusions:

• RMFTWDFA is a highly effective and time-saving algorithm for multifractal analysis of long time series.
• The method provides accurate results comparable to existing techniques.
• RMFTWDFA offers a practical tool for analyzing complex biological data, such as genomic sequences.