Intervention analysis for low-count time series with applications in public health

It is common in many fields to be interested in the evaluation of the impact of an intervention over a particular phenomenon. In the context of classical time series analysis, a possible choice might be intervention analysis, but there is no analogous methodology developed for low-count time series. In this article, we propose a modified INAR model that allows us to quantify the effect of an intervention, and is also capable of taking into account possible trends or seasonal behaviour. Several examples of application in different real and simulated contexts will also be discussed.

Integer-valued AR processes with Hermite innovations and time-varying parameters: An application to bovine fallen stock surveillance at a local scale

In this article we present a new INteger-valued AutoRegressive (INAR) model with the aim of extracting baseline patterns of cattle fallen stock registered over an 5-year period at a local scale. We introduce HINAR as a generalization of the classical Poisson-based INAR models whose innovations follow a Hermite distribution. In order to assess trends and seasonality in these time series, we fit different models with time-dependent parameters by specifying proper functions. Using real world examples, we illustrate how to estimate parameters by maximum likelihood and validate the fitted models. We also show a detailed method to forecast. Our proposed model supposes a good solution for studying discrete time series when the counts have many zeros, low counts and moderate overdispersion. This model has been applied to the analysis of fallen cattle registered at a local scale as part of the development of a veterinary syndromic surveillance system.