Superpositioned stationary count time series

Document Type

Article

Publication Date

7-1-2021

Abstract

This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

Publication Title

Probability in the Engineering and Informational Sciences

Volume

35

Issue

3

First Page

538

Last Page

556

Digital Object Identifier (DOI)

10.1017/S0269964819000433

ISSN

02699648

E-ISSN

14698951

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