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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English English |
| Published: |
College of Statistical and Actuarial Sciences, University of Punjab
2018
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| Subjects: | |
| 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 |
| Summary: | 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. |
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