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First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties
Author(s) -
Alzaid A.,
AlOsh M.
Publication year - 1988
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1988.tb01521.x
Subject(s) - mathematics , autoregressive model , unimodality , combinatorics , integer (computer science) , order (exchange) , compound poisson distribution , distribution (mathematics) , statistics , discrete mathematics , poisson regression , mathematical analysis , computer science , population , demography , finance , sociology , economics , programming language
Some properties of a first‐order integer‐valued autoregressive process (INAR)) are investigated. The approach begins with discussing the self‐decomposability and unimodality of the 1‐dimensional marginals of the process {X n } generated according to the scheme X n =α° X n ‐i +e n , where α° X n‐1 denotes a sum of X n ‐ 1 , independent 0 ‐ 1 random variables Y (n‐1) , independent of X n‐1 with Pr ‐( y (n ‐ 1) = 1) = 1 ‐ Pr ( y (n‐i) = 0) =α. The distribution of the innovation process ( e n ) is obtained when the marginal distribution of the process ( X n ) is geometric. Regression behavior of the INAR(1) process shows that the linear regression property in the backward direction is true only for the Poisson INAR(1) process.