flu forecasting with nonlinear time series analysis

Every year influenza cases spike during flu season. For public health planning one might desire to forecast the number of cases given the current situation. Regressive approaches to time series forecasting (e.g. ARMA) could be used for the task however they cannot cleanly incorporate knowledge of seasonal dynamics.

Delay coordinate embedding is an approach which takes a time series and reconstructs its dynamics in a (higher) dimensional representation space. The dynamics of trajectories in that space are diffeomorphic to the original state space dynamics. An investigation was done to see how well this dynamics based approach performed in forecasting influenza. Click here for further details.

The figure above shows the embedding dimension and delay one should use for making a forecast N weeks out. The delay (y axis), how far back data should be used for prediction, is ~1-2 weeks for predictions out to about 3 weeks (forecast). For predictions a month or more out a delay of about a year is better. Put more simply, just using data the delayed coordinate embedding suggested something which matches human intuition: for making near term predictions use current data but for long term predictions use seasonal trends.