An integer-valued pth-order autoregressive structure (INAR(p)) process

Abstract

An extension of the INAR(1) process which is useful for modelling discrete-time dependent counting processes is considered. The model investigated here has a form similar to that of the Gaussian AR(p) process, and is called the integer-valued pth-order autoregressive structure (INAR(p)) process. Despite the similarity in form, the two processes differ in many aspects such as the behaviour of the correlation, Markovian property and regression. Among other aspects of the INAR(p) process investigated here are the limiting as well as the joint distributions of the process. Also, some detailed discussion is given for the case in which the marginal distribution of the process is Poisson.

Do leading or lagging firms learn more from exporting?

“…We therefore turn to a dynamic longitudinal model to deal with serial correlation. We incorporate an integer‐valued autoregressive (INAR) process that includes lagged values of the dependent variable as regressors (see Alzaid and Al‐Osh, 1990). 13 Including firm dynamics provides three general benefits.…”

“…Al‐Osh and Alzaid (1987) and Brännäs and Hellström (2001) argue that the traditional first‐order autoregressive (AR(1)) model can be extended to the first‐order integer‐valued autoregressive (INAR(1)) model applied to count data. Moreover, Alzaid and Al‐Osh (1990) refine an integer‐valued p th‐order autoregressive structure (INAR(p)) process and address differences between the INAR(p) and AR(p) processes. We apply the INAR(p) process to our negative binomial model.…”

Innovation and Market Structure in the Manufacturing Sector: An Application of Linear Feedback Models*

“…Furthermore, Blundell et al. (2002) have extended the quasi‐differencing GMM estimator, showing that model can be transformed into a dynamic count panel data model with predetermined regressors by introducing dynamics based on the integer‐valued autoregressive (INAR) process (for INAR models, see Al‐Osh and Alzaid, 1987; Alzaid and Al‐Osh, 1990; Jin‐Guan and Yuan, 1991). The dynamic count panel data model they have proposed is in the form of a linear feedback model (LFM) and is defined as (of order p ): …”

Tests for Structural Changes in Time Series of Counts

“…The INAR(1) model was first put forward by McKenzie () and later studied in detail by Al–Osh & Alzaid () and Alzaid & Al–Osh (). It was further generalized to higher‐order models by Alzaid & Al–Osh () and Du & Li (). Related review articles are by McKenzie () and Weiss ().…”