Mean Reversion and Heavy Tails: Characterizing Time-Series Data Using Ornstein-Uhlenbeck Processes and Machine...

Area of Science:

• Time-series analysis
• Machine learning
• Stochastic processes
• Data science

Background:

• Characterizing local dynamics in time-series data is crucial for understanding complex systems.
• Traditional methods often assume stationarity, limiting their applicability to real-world, dynamic signals.
• Existing techniques may require domain-specific tuning, hindering broad application.

Purpose of the Study:

• To develop a supervised learning method for estimating local time-series dynamics.
• To quantify mean-reversion rate (θ) and heavy-tail behavior (α) from short data windows.
• To create a robust and adaptable diagnostic tool for signal processing applications.

Main Methods:

• Trained gradient-boosted tree models (CatBoost) on synthetic Ornstein-Uhlenbeck processes with α-stable noise.
• Mapped window-level statistical features to discrete categories of α and θ.
• Validated robustness for non-Gaussian and heavy-tailed time-series data.

Main Results:

• Achieved high accuracy in estimating α and θ, with predominantly adjacent-class confusion.
• Successfully applied the method to diverse real-world datasets: financial returns, sunspot numbers, and climate fields.
• Detected significant regime changes and local dynamic shifts in financial markets, solar cycles, and climate patterns.

Conclusions:

• The developed framework provides a compact and accurate diagnostic tool for time-series signal processing.
• It effectively characterizes local variability and detects regime changes without domain-specific tuning.
• Enables informed decision-making in non-stationary environments by analyzing short data windows.