On shifted integer-valued autoregressive model for count time series showing equidispersion, underdispersion or overdispersion

Abstract

In this paper, we introduce a first order integer-valued autoregressive process with Borel innovations based on the binomial thinning. This model is suitable to modeling zero truncated count time series with equidispersion, underdispersion and overdispersion. The basic properties of the process are obtained. To estimate the unknown parameters, the Yule-Walker (YW), conditional least squares (CLS) and conditional maximum likelihood (CML) methods are considered. The asymptotic distribution of CLS estimators are obtained and hypothesis tests to test an equidispersed model against an underdispersed or overdispersed model are formulated. A Monte Carlo simulation is presented analyzing the estimators performance in finite samples. Two applications to real data are presented to show that the Borel INAR(1) model is suited to model underdispersed and overdispersed data counts.