Leveraging information storage to select forecast-optimal parameters for delay-coordinate reconstructions.

Area of Science:

• Nonlinear Dynamics
• Time Series Analysis
• Predictive Modeling

Background:

• Delay-coordinate reconstruction is a key technique for nonlinear time series forecasting.
• Existing parameter estimation methods are often suboptimal for forecasting purposes.

Purpose of the Study:

• To propose an alternative strategy for selecting optimal time delay and embedding dimension parameters.
• To enhance the accuracy of forecasting models based on delay-coordinate reconstructions.

Main Methods:

• Proposed a novel method based on maximizing shared information between delay vectors and future system states.
• Applied the method to synthetic and experimental datasets.

Main Results:

• The shared information maximization metric is computationally efficient and reliable.
• The method effectively identifies optimal reconstruction parameters for forecasting.
• Demonstrated improved forecasting performance compared to traditional heuristics.

Conclusions:

• The proposed method offers a direct and effective way to optimize delay-coordinate reconstruction for forecasting.
• This approach allows practitioners to maximize predictive information and avoid reconstruction pathologies.