Quasi-Likelihood Inference for Negative Binomial Time Series Models

Temporal Changes in Invasive Group B Streptococcus Serotypes: Implications for Vaccine Development

“…A non-linear model was used to model the monthly incidence (per 1,000 live births) of GBS during the study period. Because EOD and LOD had smaller monthly incidence rates, we fitted the INGARCH model to this data [25]. A 5-term moving average was used to highlight trends in HIV-exposed and unexposed infants, and for serotype distributions.…”

Negative Binomial Quasi‐Likelihood Inference for General Integer‐Valued Time Series Models

“…Equation (2.2), which is driven by the ‐martingale difference , appears to be an infinite nonlinear autoregression with an integer‐valued solution . In fact, model (2.1)–(2.2) is very general and encompasses many important classes of integer‐valued time series models such as the (stable) Poisson INGARCH model (Grunwald et al, ; Rydberg and Shephard, ; Heinen, ; Ferland et al, ), the general Poisson autoregression (Doukhan et al, ; Doukhan and Kengne, ; Kengne, ), the stable negative binomial 2 INGARCH model (Zhu, ; Christou and Fokianos, ; Davis and Liu, ; Diop and Kengne, ), and the INAR model (McKenzie, ; Al‐Osh and Alzaid, ).…”

“…The first one is the class of models based on integer‐valued regressions such as generalized ARMA (GARMA) models, Poisson autoregression, and especially Poisson integer generalized conditional heteroskedastic (INGARCH) models (e.g. Grunwald et al, ; Rydberg and Shephard, ; Benjamin et al, ; Heinen, ; Ferland et al, ; Fokianos et al, ; Zhu, , ,b; Doukhan et al, ; Christou and Fokianos, ; Davis and Liu, ; Chen et al, ). The second class, however, concerns stochastic difference equations involving the thinning operator, of which the best known example is the integer AR (INAR) model (e.g.…”

“…Moreover, these estimates are compared in finite samples via some simulation experiments. An application to the number of transactions of the Ericsson B stock (Transaction data, Fokianos et al, ; Christou and Fokianos, ) under the negative binomial INGARCH framework is considered. For another application to the number of poliomyelitis cases in the United States (Polio data, Zeger, ), see an online Supporting Information to this paper.…”

Testing Parameter Change in General Integer‐Valued Time Series

“…We refer to Ferland et al (), Weiß (), Fokianos and Tjøstheim (), Doukhan et al (), Zhu (), Fokianos and Neumann (), Fried et al (), and so on for some recent works on Poisson autoregressive models. Moysiadis and Fokianos () studied the problem of ergodicity, stationarity in binary and categorical time series models with feedback, whereas Christou and Fokianos () investigated inference and diagnostics for negative binomial autoregressive models. Also, see Davis and Wu () and Zhu () for models with negative binomial and a distribution with zero‐inflated characteristic for modeling data with excess zeros.…”