Model-free prognostication of non-linear time series

Area of Science:

• Epidemiology
• Complex Systems Analysis
• Time Series Forecasting

Background:

• The COVID-19 pandemic underscored the need for effective infectious disease progression analysis.
• Traditional epidemiological models require data fitting, yet direct evaluation of noisy, non-linear time series is possible.
• Short-term forecasting capabilities are essential for practical epidemiological analytics.

Purpose of the Study:

• To evaluate a novel, model-independent approach for analyzing and forecasting non-linear time series.
• To assess the utility of time-lagged analyses and feature-space plots for predicting disease spread.
• To determine if machine learning can provide accurate short-range forecasts without traditional model-building.

Main Methods:

• Utilized normalized new infections per day (7-day moving average per million inhabitants) from Our World in Data.
• Applied time-lagged analyses and feature-space plots incorporating time-lagged data.
• Validated the method on unrelated non-linear time series from stock markets and blowfly populations.

Main Results:

• Machine learning models achieved excellent progression predictions using approximately 80% of time series data for training.
• Feature-space plots, after dynamic calibration, showed spikes in the maximum local Lyapunov exponent coinciding with infectious spread peaks.
• Average mutual information analysis revealed anticipatory signals for new infection peaks over various time lags and wavelengths.

Conclusions:

• Non-linear time series analysis can extract predictive characteristics for short-range forecasting without model-building.
• Time-lagged analysis offers a robust foundation for analyzing complex temporal data.
• Machine learning approaches demonstrated superior prognosticative performance in this model-independent framework.