Multivariate endemic-epidemic models with higher-order lags and an application to outbreak detection
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Multivariate time series models are an important tool for the analysis of routine public health surveillance data. We extend the endemic-epidemic framework, a class of multivariate autoregressive models for infectious disease counts, by including higher-order lags. Several parsimonious parameterizations motivated from serial interval distributions are explored. The added flexibility considerably improves the model fit and forecast performance in a case study on weekly norovirus and rotavirus counts in twelve districts of Berlin. New methodology based on periodically stationary moments is proposed and applied to investigate the goodness-of-fit of the different models. This motivates a novel approach to prospective multivariate outbreak detection as illustrated in a reanalysis of our case study.
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