When it comes to incidence data, most of the work on this field focuses on the modeling of nonextreme periods. Several attempts have been made and a variety of techniques are available to achieve so. In this work, in order to model not only the nonextreme periods but also capture the behavior of the whole time-series, we make use of a dataset on influenza-like illness rate for Greece, for the period 2014-2016. The identification of extreme periods is made possible via changepoint detection analysis and model selection techniques are developed in order to identify the optimal periodic-type auto-regressive moving average model with covariates that best describes the pattern of the time-series. In addition, in the context of incidence data modeling, an advanced algorithm was developed in order to improve the accuracy of the selected model. The derived results are satisfactory since the changepoint method seems to identify correctly the extreme periods, and the selected model: (1) estimates accurately the influenza-like illness syndrome morbidity burden in the case of Greece, and (2) captures satisfactorily enough the behavior of the whole time-series.
Keywords: Auto-regressive moving average process; changepoint detection analysis; epidemic modeling; incidence data; information criteria; model selection; periodic modeling; time-series.