Multivariate count time series models are an important tool for the
analysis and prediction of infectious disease spread. We
consider the endemic-epidemic framework, an autoregressive model
class for infectious disease surveillance counts, and replace the default
autoregression on counts from the previous time period with more
flexible weighting schemes inspired by discrete-time serial interval
distributions. We employ three different parametric formulations,
each with an additional unknown weighting parameter estimated via a profile
likelihood approach, and compare them to an unrestricted
nonparametric approach. The new methods are illustrated in a
univariate analysis of dengue fever incidence in San Juan, Puerto
Rico, and a spatio-temporal study of viral gastroenteritis in the
twelve districts of Berlin. We assess the predictive performance of
the suggested models and several reference models at various forecast horizons.
In both applications, the performance of the endemic-epidemic models is considerably
improved by the proposed weighting schemes.
This is joint work with Johannes Bracher.