Parameter inference from a non-stationary unknown process.

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Statistical Modeling

Background:

• Non-stationary systems, prevalent in climate and neuroscience, necessitate advanced analytical methods.
• Existing time-series analysis often assumes stationarity, limiting applications in dynamic real-world scenarios.
• Parameter Inference from Non-stationary Unknown Processes (PINUP) is a critical challenge.

Purpose of the Study:

• To review, unify, and categorize existing algorithms for PINUP.
• To identify limitations of current methods and propose more challenging benchmarks.
• To guide future research in analyzing non-stationary phenomena.

Main Methods:

• Categorization of PINUP algorithms into six groups: dimension reduction, statistical features, prediction error, phase-space partitioning, recurrence plots, and Bayesian inference.
• Evaluation of common benchmark systems (Lorenz process, logistic map) demonstrating their inadequacy for assessing algorithmic performance.
• Identification of more robust test cases for advancing PINUP methodologies.

Main Results:

• Existing methods often perform well on simple non-stationary systems due to basic statistical features.
• A unified framework for PINUP algorithms is presented, facilitating literature review and method comparison.
• Challenging problems were identified where current methods exhibit significant performance limitations.

Conclusions:

• The study synthesizes diverse PINUP research, revealing gaps and promoting systematic evaluation.
• Common benchmarks are insufficient; more complex systems are needed to drive methodological progress.
• This work provides a foundation for advancing the analysis of non-stationary systems and PINUP.