A New Integer-Valued Auto-Regressive Model Based on Binomial Thinning Operator

Abstract

The integer-valued time series appears in many areas of real life, for example, medical care, economics, transportation, insurance, finance, and so on. Especially, we are in the big data period and all kinds of dispersed integer-valued data may appear everyday. The thinning operator is the main method to study the integer-valued time series. In this paper, we propose a new stationary integer-valued first-order auto-regressive (INAR(1)) model based on binomial thinning operator. The model is constructed by considering the innovation to fit different dispersed data. The definition and statistical properties of the model are given. The maximum likelihood method is applied to estimate the parameters. We considered one specific model, in which the innovation follows geometric distribution, which can deal with over-dispersed integer-valued time series data. The performance of CML estimators are evaluated by simulation study. An application is given to an offence data in Track 1706 in Pittsburgh.