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

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.

Enhancing the monitoring of fallen stock at different hierarchical administrative levels: an illustration on dairy cattle from regions with distinct husbandry, demographical and climate traits

“…In many European countries, bovine fallen stock data have been gathered consistently over several years by carcass disposal services, covering a significant proportion of active farms. The potential use of bovine fallen stock data for AHSyS was described in previous studies [7][8][9][10][11][12]. In [9,11], some authors also demonstrated the usefulness of these methods for assessing the impact of past events, such as the incursion of bluetongue or the heat waves in 2003 and 2006 in the French cattle population.…”

“…This AHSyS approach involves the continuous analysis of mortality data registered at farm level. The potential of mortality data for this purpose has been demonstrated in previous studies conducted in a number of European countries [7][8][9][10][11][12]. In Catalonia (North-Eastern Spain), patterns of fallen bovine were modelled, for the main cattle production types between 2006 and 2013, using time series analyses [7,8].…”

The predictive distributions of thinning‐based count processes

“…Another example is the Hermite distribution, which is used by Fernández-Fontelo et al (2017) in INAR models as the distribution of the innovation t . Such a distribution has a log.…”

Response to the letter of “Under‐reported data analysis with INAR‐hidden Markov chains”

“…Then, the marginal distribution of the resulting under‐reported model (ω = 1) is overdispersed and Hermite distributed, as well. An example of an INAR(1) model with Hermite distributed innovations can be found in the work of Fernández‐Fontelo et al…”