Coherent forecasting in integer time series models

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Count Time Series Models (2012, background): “It is clear that the above formulation, although similar to a Poisson–loglinear model, reveals that the observed data are overdispersed. Estimation of all unknown parameters is discussed by Zeger (1988). Further detailed study of model (38) can be found in in Davis et al.”
Binomial thinning models for integer time series (2006, methodology): “The conditional mean (regression) function for this model is nonlinear, so that it is not a member of the CLAR class [Jung and Tremayne, 2006, Equation (7)].”
Integer-valued autoregressive models for counts showing underdispersion (2013, background): “3 Example (gold particles counts) Let us briefly consider the time series of gold particles counts of length T = 370 as being discussed by Jung and Tremayne [17].”
Model Selection, Estimation and Forecasting in INAR(p) Models: (2008, methodology): “More recently, Jung and Tremayne (2006) proposed a simulation based method for producing coherent forecasts for higher-order INAR models but this too requires considerable computational work and does not use likelihood methods.”
MCMC for Integer‐Valued ARMA processes (2007, unknown): “The data were originally published in Westgren (1916) but have recently been analysed in Jung and Tremayne (2006) using the method of moments estimation of an INAR(2) model.”