Moment properties and quadratic estimating functions for integer-valued time series models

Recently, there has been a growing interest in integer-valued time series models. In this paper, using a martingale difference, we prove a general theorem on the moment properties of a class of integer-valued time series models. This theorem not only contains results in the recent literature as sp...

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Main Authors:	Mohamad, Nurul Najihah, Mohamed, Ibrahim, Haur, Ng Kok
Format:	Article
Language:	English English English
Published:	College of Statistical and Actuarial Sciences, University of Punjab 2018
Subjects:	Q Science (General) QA Mathematics
Online Access:	http://irep.iium.edu.my/65037/ http://irep.iium.edu.my/65037/ http://irep.iium.edu.my/65037/ http://irep.iium.edu.my/65037/1/65037_Moment%20Properties%20and%20Quadratic%20Estimating%20Functions%20_article.pdf http://irep.iium.edu.my/65037/2/65037_Moment%20Properties%20and%20Quadratic%20Estimating%20Functions%20_scopus.pdf http://irep.iium.edu.my/65037/13/65037_Moment%20properties%20and%20quadratic%20estimating%20functions_WoS.pdf

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recordtype	eprints
spelling	iium-650372018-11-01T08:38:11Z http://irep.iium.edu.my/65037/ Moment properties and quadratic estimating functions for integer-valued time series models Mohamad, Nurul Najihah Mohamed, Ibrahim Haur, Ng Kok Q Science (General) QA Mathematics Recently, there has been a growing interest in integer-valued time series models. In this paper, using a martingale difference, we prove a general theorem on the moment properties of a class of integer-valued time series models. This theorem not only contains results in the recent literature as special cases but also has the advantage of a simpler proof. In addition, we derive the closed form expressions for the kurtosis and skewness of the models. The results are very useful in understanding the behaviour of the processes involved and in estimating the parameters of the models using quadratic estimating functions (QEF). Specifically, we derive the optimal function for the integer-valued GARCH (p, q) known as INGARCH (p, q) model. Simulation study is carried out to compare the performance of QEF estimates with corresponding maximum likelihood (ML) and least squares (LS) estimates for the INGARCH (1,1) model with different sets of parameters. Results show that the QEF estimates produce smaller standard errors than the ML and LS estimates for small sample size and are comparable to the ML estimates for larger sample size. For illustration, we fit the 108 monthly strike data to INGARCH (1, 1) models via QEF, ML and LS methods, and show the applicability of QEF method in practice. College of Statistical and Actuarial Sciences, University of Punjab 2018 Article PeerReviewed application/pdf en http://irep.iium.edu.my/65037/1/65037_Moment%20Properties%20and%20Quadratic%20Estimating%20Functions%20_article.pdf application/pdf en http://irep.iium.edu.my/65037/2/65037_Moment%20Properties%20and%20Quadratic%20Estimating%20Functions%20_scopus.pdf application/pdf en http://irep.iium.edu.my/65037/13/65037_Moment%20properties%20and%20quadratic%20estimating%20functions_WoS.pdf Mohamad, Nurul Najihah and Mohamed, Ibrahim and Haur, Ng Kok (2018) Moment properties and quadratic estimating functions for integer-valued time series models. Pakistan Journal of Statistics and Operation Research, 14 (1). pp. 157-175. ISSN 1816-2711 E-ISSN 2220-5810 http://www.pjsor.com/index.php/pjsor/article/view/1750/634 10.18187/pjsor.v14i1.1750
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	Q Science (General) QA Mathematics
spellingShingle	Q Science (General) QA Mathematics Mohamad, Nurul Najihah Mohamed, Ibrahim Haur, Ng Kok Moment properties and quadratic estimating functions for integer-valued time series models
description	Recently, there has been a growing interest in integer-valued time series models. In this paper, using a martingale difference, we prove a general theorem on the moment properties of a class of integer-valued time series models. This theorem not only contains results in the recent literature as special cases but also has the advantage of a simpler proof. In addition, we derive the closed form expressions for the kurtosis and skewness of the models. The results are very useful in understanding the behaviour of the processes involved and in estimating the parameters of the models using quadratic estimating functions (QEF). Specifically, we derive the optimal function for the integer-valued GARCH (p, q) known as INGARCH (p, q) model. Simulation study is carried out to compare the performance of QEF estimates with corresponding maximum likelihood (ML) and least squares (LS) estimates for the INGARCH (1,1) model with different sets of parameters. Results show that the QEF estimates produce smaller standard errors than the ML and LS estimates for small sample size and are comparable to the ML estimates for larger sample size. For illustration, we fit the 108 monthly strike data to INGARCH (1, 1) models via QEF, ML and LS methods, and show the applicability of QEF method in practice.
format	Article
author	Mohamad, Nurul Najihah Mohamed, Ibrahim Haur, Ng Kok
author_facet	Mohamad, Nurul Najihah Mohamed, Ibrahim Haur, Ng Kok
author_sort	Mohamad, Nurul Najihah
title	Moment properties and quadratic estimating functions for integer-valued time series models
title_short	Moment properties and quadratic estimating functions for integer-valued time series models
title_full	Moment properties and quadratic estimating functions for integer-valued time series models
title_fullStr	Moment properties and quadratic estimating functions for integer-valued time series models
title_full_unstemmed	Moment properties and quadratic estimating functions for integer-valued time series models
title_sort	moment properties and quadratic estimating functions for integer-valued time series models
publisher	College of Statistical and Actuarial Sciences, University of Punjab
publishDate	2018
url	http://irep.iium.edu.my/65037/ http://irep.iium.edu.my/65037/ http://irep.iium.edu.my/65037/ http://irep.iium.edu.my/65037/1/65037_Moment%20Properties%20and%20Quadratic%20Estimating%20Functions%20_article.pdf http://irep.iium.edu.my/65037/2/65037_Moment%20Properties%20and%20Quadratic%20Estimating%20Functions%20_scopus.pdf http://irep.iium.edu.my/65037/13/65037_Moment%20properties%20and%20quadratic%20estimating%20functions_WoS.pdf
first_indexed	2023-09-18T21:32:17Z
last_indexed	2023-09-18T21:32:17Z
_version_	1777412590416166912

Moment properties and quadratic estimating functions for integer-valued time series models

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