Estimation in conditional first order autoregression with discrete support

Abstract

Bias correction, Estimation, INAR models, Overdispersion, Small sample properties, Time series of counts,

Thinning operations for modeling time series of counts—a survey

“…. , X T , model estimation can be done, among others, by the following three approaches; see also Al-Osh and Alzaid (1987) and Jung et al (2005). First, the model parameters can be estimated by the method of moments (MM), i.e., the parameters are estimated from empirical mean, variance and first-order autocorrelation, considering the relations of Table 2.…”

“…Corresponding standard errors can be computed from the observed Fisher information. An extensive comparative study of properties and performance of these and different types of estimators was provided by Jung et al (2005).…”

The INARCH(1) Model for Overdispersed Time Series of Counts

“…We restrict to the period from January 1994 to December 2002 (108 observations), which was already investigated by (Jung et al, 2005). A line plot of the data is shown in Figure 4 (a),…”

“…(Jung et al, 2005) fitted a Poisson INAR(1) model to the data, but since the estimates obtained with different methods deviated heavily from each other, they concluded that such a model is not appropriate. And in fact, see (Jung et al, 2005), the data exhibits overdispersion (the empirical variance equals 7.92, being much larger than the mean 4.94), making the Poisson marginal distribution an unreasonable choice, also see Figure 4 (d).…”

A Poisson INAR(1) process with a seasonal structure

“…The INAR model has been extensively studied in the literature. For example, see the survey by Weiß, [3] Jung et al [4] and Freeland and McCabe. [5] Monteiro et al [6] had proposed the The process {Y t } t∈Z in Equation (1) has two random components: the survivors of the elements of the process at time t − s, given by φ • Y t−s , each with probability φ of survival, and the elements which entered the system in the interval (t − s, t], defining the innovation term ǫ t .N o t e that the INAR(1) model [2] is a particular case of the INAR(1) s when s = 1.…”