First order autoregressive time series with negative binomial and geometric marginals

On Shifted Geometric INAR(1) Models Based on Geometric Counting Series

“…• Zero truncated Poisson INAR(1) model (Bakouch and Ristić, 2010) • Iterated INAR(1) model with negative binomial marginals (Al-Osh and Aly, 1992); and • Random Coefficient INAR(1) model with negative binomial marginals (Weiß, 2008).…”

Higher-order moments, cumulants and spectral densities of the NGINAR(1) process

“…The importance of these series comes in simulating realizations of such geometric time series in various branches of science: e.g., insurance theory, medicine, queueing systems, communications, reliability theory, reservoirs theory and precipitation modelling. Several authors, such as McKenzie [4][5][6] and Al-Osh and Aly [1], have introduced integer-valued time series with negative binomial and geometric marginals as contributions to such time series. They study the geometric AR(1) model using the binomial thinning operator which contains Bernoulli counting series.…”

A COMBINED SDLINAR(p) MODEL AND IDENTIFICATION AND PREDICTION OF ITS LATENT COMPONENTS

“…To the present day, there is a variety of INAR models with different marginals. McKenzie [15], Du and Li [9] and AlOsh and Alzaid [1] analyzed models with negative binomial and geometric marginals. Freeland and McCabe [11] studied model with Poisson marginals, Ristić et al [18] introduced a process with geometric marginals based on a negative binomial thinning operator.…”

“…Then, Nastić et al [17] studied a processes with symmetric discrete Laplace marginals and BarretoSouza and Bourguignon [3] processes with skew discrete Laplace marginals. Djordjević [8] gave a generalization of series with discrete Laplace marginal distribution defining SDLIN AR (1), a model with all four different parameters.…”