Dynamic hierarchical state space forecasting.

Area of Science:

• Statistics
• Epidemiology
• Computational Science

Background:

• Accurate time series forecasting is crucial for public health and resource allocation.
• Existing methods often struggle with incorporating external information and unit-specific historical data effectively.
• Understanding disease dynamics requires models that can adapt to evolving patterns.

Purpose of the Study:

• To develop a novel time series forecasting model that borrows information from related units while incorporating target unit history.
• To improve the accuracy of forecasts by utilizing shared patterns aligned by an internal time index.
• To provide a flexible framework for forecasting in situations with multiple related time series.

Main Methods:

• A hierarchical state space model was constructed for multiple time series data.
• A conditional state space model was developed to integrate external unit information as prior knowledge.
• Kalman filtering was applied to the conditional state space model for forecasting.
• Forecasts were transformed from internal time to calendar time for interpretability.

Main Results:

• The proposed model effectively incorporates information from existing units and the target unit's history.
• Simulation studies demonstrated the finite sample performance of the method.
• The approach showed promise in forecasting state-level new COVID-19 cases in the United States.

Conclusions:

• The developed method offers an effective way to enhance time series forecasting by leveraging cross-unit information.
• This approach provides a robust framework for epidemiological forecasting and other applications with multiple related time series.
• The integration of internal time alignment and hierarchical modeling offers a significant advancement in forecasting accuracy.