Combining multiple forecasts for multivariate time series via state-dependent weighting.

Area of Science:

• Dynamical systems
• Time series analysis
• Machine learning

Background:

• Forecast accuracy is often limited by fixed weighting schemes.
• Existing methods struggle to adapt forecast combinations dynamically to changing system states.
• State-space position is a critical but often overlooked factor in forecast performance.

Purpose of the Study:

• To develop a model-free algorithm for dynamically combining multiple forecasts.
• To leverage state-space positioning for adaptive forecast weighting.
• To enhance prediction accuracy in complex systems and real-world applications.

Main Methods:

• A novel algorithm dynamically combines forecasts using multivariate time series data.
• Forecasts are weighted locally based on their position in a reconstructed state space.
• A local loss function evaluates forecast error discounted by spatial distance, unlike time-based methods.
• Forecast selection at each time step utilizes an enhanced multiview embedding approach.

Main Results:

• The proposed method achieved the lowest mean squared error for the Rössler and Lorenz'96I models compared to ensemble methods.
• In flood forecasting, the algorithm demonstrated superior accuracy against conventional machine learning techniques.
• The method successfully predicted maximum river water levels without prior knowledge, showcasing its robustness.

Conclusions:

• The developed algorithm offers a significant advancement in model-free time series forecasting.
• Dynamic, state-space-aware weighting improves prediction accuracy over traditional methods.
• This approach holds promise for reliable forecasting in environmental and complex dynamical systems.