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Summary
This summary is machine-generated.

This study introduces a supervised learning method to analyze time-series dynamics using mean-reversion rate (θ) and heavy-tail (α) estimates. The approach accurately detects changes in financial, solar, and climate data, offering a versatile signal processing tool.

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GaussianLévyOrnstein–Uhlenbeckcomplexity metricsmachine learningmean reversion

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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.