Journal ArticleDOI
First-order integer-valued autoregressive (inar(1)) process
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In this paper, a simple model for a stationary sequence of integer-valued random variables with lag-one dependence is given and is referred to as the INAR(1)) process.Abstract:
. A simple model for a stationary sequence of integer-valued random variables with lag-one dependence is given and is referred to as the integer-valued autoregressive of order one (INAR(1)) process. The model is suitable for counting processes in which an element of the process at time t can be either the survival of an element of the process at time t - 1 or the outcome of an innovation process. The correlation structure and the distributional properties of the INAR(1) model are similar to those of the continuous-valued AR(1) process. Several methods for estimating the parameters of the model are discussed, and the results of a simulation study for these estimation methods are presented.read more
Citations
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Individual effects and dynamics in count data models
TL;DR: In this article, the authors examined the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables, and used a linear feedback model to obtain a consistent estimator for the parameters in the dynamic model.
Journal ArticleDOI
THE INTEGER‐VALUED AUTOREGRESSIVE (INAR(p)) MODEL
Du Jin-Guan,Li Yuan +1 more
TL;DR: In this article, the existence and ergodic properties of the integer-valued autoregressive model with lag p dependence were proved and it was shown that the correlation structure of the INAR model is similar to that of the continuous-valued auto-regression process.
Journal ArticleDOI
Thinning operations for modeling time series of counts—a survey
TL;DR: In this paper, a review of binomial thinning operations and their application to integer-valued ARMA models is presented. But this paper is restricted to the case of Poisson counts.
Journal ArticleDOI
Some arma models for dependent sequences of Poisson counts
TL;DR: In this article, a family of models for discrete-time processes with Poisson marginal distributions is developed and investigated, and the joint distribution of n consecutive observations in a process is derived and its properties discussed.
Journal ArticleDOI
Recent developments in count data modelling: theory and application
TL;DR: In this paper, statistical methods for modeling individual behavior when the endogenous variable is a nonnegative integer are discussed with a focus on specification, estimation, and testing, and an application to labor mobility data illustrates the gain obtained by carefully taking into account the specific structure of the data.
References
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Discrete analogues of self-decomposability and stability
FW Fred Steutel,van K Klaas Harn +1 more
TL;DR: In this paper, analogues for the concepts of self-decomposability and stability for distributions on the nonnegative integers were proposed, and it turns out that these "discrete self-Decomposable" and "Discrete Stable" distributions have properties that are quite similar to those of their continuous counterparts.
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On Conditional Least Squares Estimation for Stochastic Processes
TL;DR: In this paper, an estimation procedure for stochastic processes based on the minimization of a sum of squared deviations about conditional expectations is developed, and the estimators and their limiting covariance matrix are worked out in detail for a subcritical branching process with immigration.
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First Order Autoregressive Gamma Sequences and Point Processes.
Donald P. Gaver,P. A. W. Lewis +1 more
TL;DR: In this paper, it is shown that there is an innovation process such that the sequence of random variables generated by the linear, additive first-order autoregressive scheme X n = pXn-1 + ∊ n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1.
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Stationary discrete autoregressive‐moving average time series generated by mixtures
TL;DR: This work is supported in part by the National Science Foundation under Grant NSF-ENG-79-01438 and NSF -79-10825 and by the Office of Naval Research under Grant NR-42-284 and NR- 42-469.
Journal ArticleDOI
A Monte Carlo study of autoregressive integrated moving average processes
Warren T. Dent,An-Sik Min +1 more
TL;DR: In this paper, the simpler ARMA type models are examined with respect to properties of a variety of proposed estimators of unknown parameters, and the authors suggest that if only one estimation method were available to a researcher, the choice should probably be maximum likelihood.