Forecasting high-dimensional dynamics exploiting suboptimal embeddings.

Area of Science:

• Dynamical Systems and Time Series Analysis
• Nonlinear Dynamics
• Forecasting Methodologies

Background:

• Delay embedding is a common model-free method for reconstructing dynamical systems and forecasting nonlinear time series.
• Existing frameworks for multivariate time series forecasting combine multiple embeddings but often lack optimal selection strategies.
• Current methods may randomly select embeddings or use brute force, neglecting embedding diversity and leading to suboptimal performance.

Purpose of the Study:

• To develop an advanced forecasting framework that addresses limitations in existing methods for multivariate time series.
• To enhance the accuracy and reliability of time series forecasting by optimizing the selection and combination of delay embeddings.
• To introduce a novel approach that leverages "suboptimal embeddings" derived from combinatorial optimization.

Main Methods:

• Development of a new forecasting framework utilizing "suboptimal embeddings".
• Employing combinatorial optimization to minimize in-sample error for embedding selection.
• Systematic evaluation of the framework against existing methods using toy and real-world datasets.

Main Results:

• The proposed framework significantly outperforms existing methods in forecasting accuracy.
• Demonstrated superior performance on both synthetic (toy) datasets and a real-world flood dataset.
• The framework shows applicability across diverse data lengths and dimensions.

Conclusions:

• The developed framework offers a superior approach to multivariate time series forecasting by intelligently combining diverse embeddings.
• This method overcomes the limitations of random selection or brute-force approaches in existing frameworks.
• The framework's versatility makes it suitable for applications in neuroscience, ecology, finance, fluid dynamics, weather, and disaster prevention.