Statistical Modelling 17 (3) (2017), 172–195

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

Amanda Fernández-Fontelo
Departament de Matemàtiques,
Universitat Autònoma de Barcelona,
Cerdanyola del Vallès,
Barcelona,
Spain
e-mail: amanda@mat.uab.cat

Sara Fontdecaba
Departament d'Estadística i Investigació Operativa,
Universitat Politècnica de Catalunya,
Barcelona,
Spain


Anna Alba
Centre de Recerca en Sanitat Animal (CReSA),
Institut de Recerca i Tecnologia Agroalimentàries (IRTA),
Campus UAB,
Bellaterra, Barcelona,
Spain


and

Department of Veterinary Population Medicine,
College of Veterinary Medicine,
University of Minnesota,
Saint Paul, Minnesota
USA


Pedro Puig
Departament de Matemàtiques,
Universitat Autònoma de Barcelona,
Cerdanyola del Vallès,
Barcelona,
Spain


Abstract:

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.
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