Gaussian and Lerch Models for Unimodal Time Series Forcasting

Area of Science:

• Statistics
• Time Series Analysis
• Epidemiological Modeling

Background:

• Unimodal time series forecasting presents unique challenges.
• Accurate modeling of infectious disease spread, such as COVID-19, is crucial for public health.
• Existing forecasting models may not fully capture the characteristics of unimodal data.

Purpose of the Study:

• To propose and evaluate Gaussian and Lerch models for unimodal time series forecasting.
• To compare parameter estimation techniques, specifically minimization of absolute residuals with and without a weighted median.
• To apply these models to forecast daily COVID-19 infections in China and derive confidence intervals.

Main Methods:

• Development of Gaussian (3-parameter) and Lerch (4-parameter) models.
• Parameter estimation via minimization of the sum of absolute residuals.
• Comparison of estimation methods: with and without a weighted median.
• Application to daily COVID-19 infection data from China.

Main Results:

• Both Gaussian and Lerch models were applied to COVID-19 daily infection data.
• Parameter estimation was performed using two distinct minimization approaches.
• Confidence intervals for daily infection forecasts were successfully derived from local minima.
• The performance comparison of the weighted median approach versus no weighted median was conducted.

Conclusions:

• The Gaussian and Lerch models offer viable approaches for unimodal time series forecasting.
• The choice of parameter estimation method (with or without weighted median) impacts model results.
• The models provide a framework for generating confidence intervals in epidemiological forecasting.
• The study demonstrates the utility of these models in a real-world application concerning COVID-19 spread.