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On mixed PARMA modeling of epidemiological time series data

Abstract A rich class of traditional statistical models and methods is currently available for the early detection of epidemic activity in epidemiological surveillance systems. Real time surveillance though, is often difficult to be fully achieved because of the seasonality involved in the series. Indeed, whenever the correlation structure of a series depends on the season, the time series involved fails to reach stationarity with all the associated modeling consequences. In such situations, a useful class of models is that of periodic auto-regressive moving average (PARMA) models allowing parameters that depend on season. In this work, for the modeling of influenza-like syndrome morbidity, the general form as well as special cases of PARMA models are considered, and via model selection identification and likelihood-based techniques, the optimal model is selected. Climatological and meteorological covariates associated with influenza-like syndrome are also incorporated into the model structure. The derived results are satisfactory since the selected model succeeds in identifying the epidemic waves, and in estimating accurately the influenza-like syndrome morbidity burden in the case of Greece (for the period 2014–2016).