Scaling Exponents of Time Series Data: A Machine Learning Approach.

Area of Science:

• Time Series Analysis
• Statistical Modeling
• Machine Learning Applications

Background:

• The Hurst exponent quantifies long-range dependence in time series data.
• Traditional methods like Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA) have limitations, especially with fractional Lévy motion.
• Existing methods often require complex preprocessing steps like power spectrum calculation.

Purpose of the Study:

• To develop a novel, machine learning-based approach for accurate Hurst exponent estimation.
• To address the limitations of traditional methods in distinguishing between fractional Lévy and fractional Brownian motion.
• To enable continuous estimation of the scaling exponent directly from time series data.

Main Methods:

• Training machine learning models (LightGBM, MLP, AdaBoost) on synthetic data with known Hurst exponents.
• Utilizing fractional Brownian motion and fractional Lévy motion for data generation.
• Directly estimating the scaling exponent from time series without power spectrum analysis.

Main Results:

• Machine learning estimators significantly outperform traditional R/S analysis and DFA.
• The proposed method shows superior accuracy, particularly for data resembling fractional Lévy motion.
• Validation on financial data revealed discrepancies with literature but confirmed the approach's accuracy against known ground truths.

Conclusions:

• Machine learning offers a powerful and accurate alternative for Hurst exponent estimation.
• This approach advances time series analysis by integrating machine learning with traditional financial methods.
• The findings open new avenues for analyzing complex time series data with enhanced precision.