Forecastability of infectious disease time series: are some seasons and pathogens intrinsically more difficult to forecast?

For infectious disease forecasting challenges, individual model performance typically varies across space and time. This phenomenon raises the question: are there properties of the target time series that contribute to a particular season, location, or disease being more difficult to forecast? Here we characterize a time series' future predictability using a forecastability metric that calculates the spectral entropy of the time series. Forecastability of syndromic influenza hospital admissions for the state of California varied widely across seasons and was positively correlated with peak burden. Next, using archived U.S. state and national forecasts targeting laboratory-confirmed COVID-19 and influenza hospital admissions, we investigated the relationship between forecastability and: (i) population size of the forecasting target, and (ii) forecast performance as measured by mean absolute error, weighted interval score (WIS), and scaled relative WIS. Forecastability increased with increasing population size of the forecasting target, and forecasting performance generally improved with higher forecastability when mitigating the effects of population size across scales. These preliminary results support the idea that some targets and respiratory virus seasons may be inherently more difficult to forecast and could help explain inter-seasonal variation in model performance.