Aligning Time-series by Local Trends: Applications in Public Health

Abstract

Individual models of infectious diseases or trajectories coming from different simulations may vary considerably, making it challenging for public communication and supporting policy-making. Therefore, it is common in public health to first create a consensus across multiple models and simulations through ensembling. However, current methods are limited to mean and median ensembles that perform aggregation of scale (cases, hospitalizations, deaths) along the time axis, which often misrepresents the underlying trajectories -- e.g., they underrepresent the peak. Instead, we wish to create an ensemble that represents aggregation simultaneously over both time and scale and thus better preserves the properties of the trajectories. This is particularly useful for public health where time-series have a sequence of meaningful local trends that are ordered, e.g., a surge to an increase to a peak to a decrease. We propose a novel alignment method DTW+SBA, which combines a representation of local trends along with dynamic time warping barycenter averaging. We prove key properties of this method that ensure appropriate alignment based on local trends. We demonstrate on real multi-model outputs that our approach preserves the properties of underlying trajectories. We also show that our alignment leads to a more sensible clustering of epidemic trajectories.