Stationary solutions for integer-valued autoregressive processes

The purpose of this paper is to introduce and develop a family of ℤ + -valued autoregressive processes of order p ( INAR ( p ) ) by using the generalized multiplication ⊙ F of van Harn and Steutel (1982). We obtain various distributional and regression properties for these models. A number of stationary INAR ( p ) processes with specific marginals are presented and are shown to generalize several existing models.

[1]  Harry Joe,et al.  A New Type of Discrete Self-Decomposability and Its Application to Continuous-Time Markov Processes for Modeling Count Data Time Series , 2003 .

[2]  Mohamed Alosh,et al.  First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties , 1988 .

[3]  E. McKenzie,et al.  Some ARMA models for dependent sequences of poisson counts , 1988, Advances in Applied Probability.

[4]  Limit theorems for the Galton-Watson process with time-dependent immigration , 1971 .

[5]  Emad-Eldin A. A. Aly,et al.  On Geometric Infinite Divisibility and Stability , 2000 .

[6]  Specialised class L property and stationary autoregressive process , 1994 .

[7]  F. Steutel,et al.  Stability equations for processes with stationary independent increments using branching processes and Poisson mixtures , 1993 .

[8]  E. Mckenzie.  Innovation distributions for gamma and negative binomial autoregressions , 1987 .

[9]  Li Yuan,et al.  THE INTEGER‐VALUED AUTOREGRESSIVE (INAR(p)) MODEL , 1991 .

[10]  Self-Decomposable Discrete Distributions and Branching Processes , 1982 .

[11]  A. J. Lawrance,et al.  The Exponential Autoregressive‐Moving Average Earma(P,Q) Process , 1980 .

[12]  Alain Latour,et al.  Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process , 1998 .

[13]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[14]  On geometric stability and poisson mixtures , 1999 .

[15]  E. McKenzie,et al.  Autoregressive moving-average processes with negative-binomial and geometric marginal distributions , 1986, Advances in Applied Probability.

[16]  A. Alzaid,et al.  Integer-valued moving average (INMA) process , 1988 .

[17]  Fw Fred Steutel,et al.  Discrete analogues of self-decomposability and stability , 1979 .

[18]  Emad-Eldin A. A. Aly,et al.  Explicit stationary distributions for some galton-watson processes with immigration , 1994 .

[19]  Stephen G Walker,et al.  A Note on the Innovation Distribution of a Gamma Distributed Autoregressive Process , 2000 .