SOME SIMPLE MODELS FOR DISCRETE VARIATE TIME SERIES¹

Abstract

Simple models are presented for use in the modeling and generation of sequences of dependent discrete random variables. The models are essentially Markov Chains, but are structurally autoregressions, and so depend on only a few parameters. The marginal distribution is an intrinsic component in the specification of each model, and the Poisson, Geometric, Negative Binomial and Binomial distributions are considered. Details are also given for the introduction of time‐dependence into the means of the sequences so that seaonality can be treated simply.

Studying the effect of weather conditions on daily crash counts using a discrete time-series model

“…However, models that capture the same idea, but suitable for count data, can be also constructed. McKenzie (1985) and Al-Osh and Alzaid (1987) defined an analogous process for discrete data, called the Integer-valued autoregressive (INAR) process as follows:…”

“…In response to these problems, we therefore present in this paper, a first-order autoregressive (AR1) time-series model for Poisson distributed data (see section 2) and compare it to some of the classical models found in the literature. The Poisson AR(1) model was first developed by Al-Osh and Alzaid (1987) and McKenzie (1985). Joe (1996) later generalized the approach.…”

Estimation and Forecasting in INAR(P) Models Using Sieve Bootstrap

“…A proposal is the integer-valued autoregressive process (INAR) (McKenzie (1985), Al-Osh and Alzaid (1987)):…”

“…The most common approach to build an integer-valued autoregressive (INAR) process is based on a probabilistic operator called binomial thinning, as reported in Al-Osh and Alzaid (1987) and McKenzie (1985) who first introduced INAR processes. While theoretical properties of INAR models with Poisson innovations have been extensively studied in the literature (see, for instance, Freeland and McCabe (2004a), , and the references therein), relatively few contributions discuss the development of methods for INAR models with innovations distributed differently from the Poisson.…”

Markov Chain Approach to Forecast in the Binomial Autoregressive Models

“…This paper considers proposed by McKenzie (1985) and is extended to a higher order by Weiß (2009). Since the binomial autoregressive model is a Markov chain, we can apply the earlier work of Bu and McCabe (2008) for integer valued autoregressive(INAR) model to the binomial autoregressive model.…”