Journal of Statistical Theory and Applications

Volume 19, Issue 3, September 2020, Pages 415 - 431

First-Order Integer-Valued Moving Average Process with Power Series Innovations

Authors
Eisa Mahmoudi*, ORCID, Ameneh Rostami
Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran
*Corresponding author. Email: emahmoudi@yazd.ac.ir
Corresponding Author
Eisa Mahmoudi
Received 5 September 2019, Accepted 19 May 2020, Available Online 28 September 2020.
DOI
10.2991/jsta.d.200917.001How to use a DOI?
Keywords
First-order integer-valued moving average process; Poisson thinning operator; Moving average model; Power series family of distributions
Abstract

In this paper, we introduce a first-order nonnegative integer-valued moving average process with power series innovations based on a Poisson thinning operator (PINMAPS(1)) for modeling overdispersed, equidispersed and underdispersed count time series. This process contains the PINMA process with geometric, Bernoulli, Poisson, binomial, negative binomial and logarithmic innovations which some of them are studied in details. Some statistical properties of the process are obtained. The unknown parameters of the model are estimated using the Yule-Walker, conditional least squares and least squares feasible generalized methods. Also, the performance of estimators is evaluated using a simulation study. Finally, we apply the model to three real data set and show the ability of the model for predicting data compared to competing models.

Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)
View full text (HTML)

Journal
Journal of Statistical Theory and Applications
Volume-Issue
19 - 3
Pages
415 - 431
Publication Date
2020/09/28
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.d.200917.001How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Eisa Mahmoudi
AU  - Ameneh Rostami
PY  - 2020
DA  - 2020/09/28
TI  - First-Order Integer-Valued Moving Average Process with Power Series Innovations
JO  - Journal of Statistical Theory and Applications
SP  - 415
EP  - 431
VL  - 19
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200917.001
DO  - 10.2991/jsta.d.200917.001
ID  - Mahmoudi2020
ER  -