A new geometric first-order integer-valued autoregressive (NGINAR(1)) process

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

“…where α * and β * are the negative binomial thinning operators, defined in [18] as α * X = X i=1 W i , where {W i } is a sequence of independent and identically distributed random variables with geometric, Geom(α/(1+α)), α ∈ (0, 1), distribution, where W i and X are independent random variables for all i 1 and β * Y = Y i=1 V i , where {V i } is a sequence of independent and identically distributed random variables with geometric, Geom(β/(1 + β)), β ∈ (0, 1), and V i and Y are independent random variables for all i 1. Random variables X and Y are independent and have geometric, Geom(µ/(1 + µ)) and Geom(ν/(1 + ν)), distributions, respectively.…”

“…time series is based on the N GIN AR(1) model, introduced by [18]. Since in the N GIN AR(1) model has the restriction that α ∈ (0, µ/(1 + µ)], the SDLIN AR(1) model must have it too.…”

“…Since in the N GIN AR(1) model has the restriction that α ∈ (0, µ/(1 + µ)], the SDLIN AR(1) model must have it too. It means that to have well-defined distribution of {e n }, as discussed in [18] and [8], it is necessary to have α ∈ (0, µ/(1 + µ)] and β ∈ (0, ν/(1 + ν)]. Random variables e n , n ≥ 1, are independent and identically distributed integervalued random variables.…”

“…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. Later, integer-valued processes with both positive and negative values appeared.…”

A new model for time series of counts

“…Brannas [4] illustrated the time series counts model with four short, annual industry series in the Swedish paper and pulp industry. Ristic et al [5] and Bakouch and Ristic [6] considered crime data, especially sex offence counts data series. Quudus [7] studied monthly car casualties within the congestion zone.…”