A New Overdispersed Integer-Valued Moving Average Model with Dependent Counting Series

Abstract

A new integer-valued moving average model is introduced. The assumption of independent counting series in the model is relaxed to allow dependence between them, leading to the overdispersion in the model. Statistical properties were established for this new integer-valued moving average model with dependent counting series. The Yule–Walker method was applied to estimate the model parameters. The estimator’s performance was evaluated using simulations, and the overdispersion test of the INMA(1) process was applied to examine the dependence between counting series.

Time Series Modelling

“…The resulting model is able to flexibly adapt to different types of dispersion behavior, which is also demonstrated by several real-data examples. Furthermore, Yu and Wang [ 13 ] consider an extension of the binomial thinning operator, achieved by allowing for a dependent counting series, and this time, the operator is used within the class of INMA models. Properties of, and estimation for, this new type of INMA model are investigated, and they are illustrated by an application to a crime-counts time series.…”