A flexible univariate moving average time-series model for dispersed count data

Kimberly F Sellers,Sean Melville,Ali Arab,Fanyu Cui

doi:10.1186/s40488-021-00115-2

Abstract

Al-Osh and Alzaid (1988) consider a Poisson moving average (PMA) model to describe the relation among integer-valued time series data; this model, however, is constrained by the underlying equi-dispersion assumption for count data (i.e., that the variance and the mean equal). This work instead introduces a flexible integer-valued moving average model for count data that contain over- or under-dispersion via the Conway-Maxwell-Poisson (CMP) distribution and related distributions. This first-order sum-of-Conway-Maxwell-Poissons moving average (SCMPMA(1)) model offers a generalizable construct that includes the PMA (among others) as a special case. We highlight the SCMPMA model properties and illustrate its flexibility via simulated data examples.

Highlights

Integer-valued thinning-based models have been proposed to model time series data represented as counts
Introducing the sCMPMA[1] model Motivated by the SCMPAR[1] model of Sellers et al (2020), we introduce a first-order sum-of-CMPs moving average (SCMPMA[1]) process Xt by
This work utilizes the sCMP distribution of Sellers et al (2017) to develop a SCMPMA[1] model that serves as a flexible moving average time series model for discrete data where data dispersion is present

Summary

Introduction

Integer-valued thinning-based models have been proposed to model time series data represented as counts. Al-Osh and Alzaid (1988) introduce a generally defined integer-valued moving average (INMA) process as an analog to the moving average (MA) model for continuous data which assumes an underlying Gaussian distribution. To form such a model, they consider the “survivals” of independent and identically distributed (iid) non-negative integer valued random innovations to maintain and ensure discrete data outcomes (Weiss 2021).

Results

Conclusion