The application of traditional forecasting methods to discrete count data yields forecasts that are non-coherent. That is, such methods produce non-integer point and interval predictions which violate the restrictions on the sample space of the integer variable. This paper presents a Bayesian methodology for producing coherent forecasts of low count time series. The forecasts are based on estim...

The application of traditional forecasting methods to discrete count data yields forecasts that are non-coherent. That is, such methods produce non-integer point and interval predictions which violate the restrictions on the sample space of the integer variable. This paper presents a methodology for producing coherent forecasts of low count time series. The forecasts are based on estimates of t...

The INteger-valued AutoRegressive (INAR) processes were introduced in the literature by Al-Osh and Alzaid (1987) and McKenzie (1988) for modelling correlated series of counts. These processes have been considered as the discrete counter part of AR processes, but their highly nonlinear characteristics lead to some statistically challenging problems, namely in parameter estimation. Several estima...

Abstract This article considers bivariate mixed Poisson INAR(1) regression models with correlated random effects for modelling correlations of different signs and magnitude among time series types claim counts. is the first that proposed family used in a statistical or actuarial context. For expository purposes, count Lognormal Gamma paired via Gaussian copula are presented as competitive alter...

☆ I thankDavid Cutler, Larry Katz, Jeff Liebman, DuncanT inar participants at Academia Sinica, Harvard, and the P ments. This research was supported by the NSF Gradu Multidisciplinary Program on Inequality and Social Polic and the NBER Aging Program (NIA Grant T32-AG000186) E-mail address: [email protected]. 1 See, for example, Persico et al. (2004) and Case and Pax Lundborg et al. (2009) on ...

Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one innovations, abbr. ZOINAR(1) processes, introduced recently, around year 2020 to present. This manuscript presents a generalization ZOINAR given introd...

where {ξn,j , εn: n, j ∈ N} are independent random variables with nonnegative integer values such that for each n ∈ N, {ξn,j : j ∈ N} are identically distributed. We can interpret Xn as the number of individuals in the n-th generation of a population, ξn,j is the number of offsprings produced by the j-th individual belonging to the (n− 1)-th generation, and εn is the number of immigrants in the...