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

Kimberly F. Sellers (), Ali Arab (), Sean Melville () and Fanyu Cui ()
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Kimberly F. Sellers: Georgetown University
Ali Arab: Georgetown University
Sean Melville: Georgetown University
Fanyu Cui: Georgetown University

Journal of Statistical Distributions and Applications, 2021, vol. 8, issue 1, 1-12

Abstract: 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.

Keywords: Over-dispersion; Under-dispersion; Conway-Maxwell-Poisson (COM-Poisson or CMP); Sum-of-Conway-Maxwell-Poisson (sCMP) (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1186/s40488-021-00115-2

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