A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of...

Full description

Bibliographic Details
Main Authors: Zhengwei Liu, Fukang Zhu
Format: Article
Language:English
Published: MDPI AG 2021-12-01
Series:Entropy
Subjects:
extended binomial distribution
INAR
thinning operator
time series of counts
Online Access:https://www.mdpi.com/1099-4300/23/1/62
id doaj-f3ba4b8e5fb9424aa1fdc0ddacd08258
record_format Article
spelling doaj-f3ba4b8e5fb9424aa1fdc0ddacd082582021-01-01T00:06:33ZengMDPI AGEntropy1099-43002021-12-0123626210.3390/e23010062A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count DataZhengwei Liu0Fukang Zhu1School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, ChinaSchool of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, ChinaThe thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.https://www.mdpi.com/1099-4300/23/1/62extended binomial distributionINARthinning operatortime series of counts
collection DOAJ
language English
format Article
sources DOAJ
author Zhengwei Liu
Fukang Zhu
spellingShingle Zhengwei Liu
Fukang Zhu
A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data
Entropy
extended binomial distribution
INAR
thinning operator
time series of counts
author_facet Zhengwei Liu
Fukang Zhu
author_sort Zhengwei Liu
title A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data
title_short A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data
title_full A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data
title_fullStr A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data
title_full_unstemmed A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data
title_sort new extension of thinning-based integer-valued autoregressive models for count data
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2021-12-01
description The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.
topic extended binomial distribution
INAR
thinning operator
time series of counts
url https://www.mdpi.com/1099-4300/23/1/62
work_keys_str_mv AT zhengweiliu anewextensionofthinningbasedintegervaluedautoregressivemodelsforcountdata
AT fukangzhu anewextensionofthinningbasedintegervaluedautoregressivemodelsforcountdata
AT zhengweiliu newextensionofthinningbasedintegervaluedautoregressivemodelsforcountdata
AT fukangzhu newextensionofthinningbasedintegervaluedautoregressivemodelsforcountdata
_version_ 1724364497933565952

Similar Items