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SUPERPOSITIONED STATIONARY COUNT TIME SERIES

Published online by Cambridge University Press:  23 December 2019

Yisu Jia Open the ORCID record for Yisu Jia [Opens in a new window] ,
Robert Lund  and
James Livsey
Yisu Jia
Affiliation:
Department of Mathematics and Statistics, University of North Florida, 1 UNF Drive, Jacksonville, FL 32224, USA E-mail: y.jia@unf.edu
Robert Lund
Affiliation:
Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, S.C. 29634-0975, USA
James Livsey
Affiliation:
U.S. Census Bureau, Center for Statistical Research and Methodology, 4600 Silver Hill Rd, Washington, DC 20233, USA
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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.

Keywords

count-valued processesnegative binomial distributionPoisson distributionstationary processestime series
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 538 - 556
Copyright
© Cambridge University Press 2019

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