Time-Varying Autoregressive Models: A Novel Approach Using Physics-Informed Neural Networks.

Area of Science:

• Statistics
• Machine Learning
• Time Series Analysis

Background:

• Traditional autoregressive (AR/VAR) models assume stationarity, which is often violated in real-world data.
• Time-varying (TV-AR/TV-VAR) models address non-stationarity but conventional estimation methods have limitations.
• Existing techniques often require restrictive assumptions about basis functions, limiting flexibility.

Purpose of the Study:

• To introduce a novel framework for modeling time-varying autoregressive processes using physics-informed neural networks (PINNs).
• To overcome limitations of conventional estimation methods for TV-AR/TV-VAR models.
• To extend the applicability of PINNs to time series analysis.

Main Methods:

• Development of a new framework leveraging physics-informed neural networks (PINNs) for TV-AR/TV-VAR modeling.
• Adaptation of the PINN framework for time series analysis, reducing reliance on explicit physical structures.
• Validation through simulations on synthetic data and analysis of real-world health data.

Main Results:

• The proposed PINN-based method effectively models time-varying autoregressive processes.
• The framework demonstrates flexibility and broader applicability compared to conventional methods.
• Successful validation on both synthetic and real-world time series data.

Conclusions:

• Physics-informed neural networks offer a powerful and flexible approach for modeling non-stationary time series.
• The novel PINN framework advances the analysis of time-varying autoregressive models.
• This method holds promise for diverse applications requiring the analysis of evolving temporal dynamics.