Investigating GQL-based inferential approaches for non-stationary BINAR(1) model under different quantum of over-dispersion with application

Khan, Naushad Mamode; Sunecher, Yuvraj; Jowaheer, Vandna; Ristić, Miroslav M.; Khan, Maleika Heenaye-Mamode

doi:10.1007/s00180-018-0836-5

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…Brännäs and Quoreshi discussed CLS, FGLS and GMM estimators, while they did not consider Maximum-Likelihood estimator since the underlying distributions of the counts were unknown. Similar argument was discussed by Mamode Khan et al [46] and Sunecher et al [47] and recommended a GQL approach to estimate the parameters. Besides, the innovation terms are unobserved and therefore likelihood computations become unfeasible.…”

Section: Discussionsupporting

confidence: 64%

“…The GQL estimating equation is sourced from the likelihood estimating equation based on the exponential dispersion family [45], consisting of three components: The score vector and its corresponding mean, the auto-covariance function and the derivative component. Under the correct specification of the expected score and auto-covariance function, the GQL approach is shown to yield asymptotically equally efficient estimates as the maximum-likelihood based approach which is as expected [46]. Besides, in Mamode Khan et al [46] and Sunecher et al [47], it is proved that GQL yields more efficient estimates than CLS.…”

Section: The Inma Binma and Vinma Models Estimationmentioning

confidence: 80%

“…Under the correct specification of the expected score and auto-covariance function, the GQL approach is shown to yield asymptotically equally efficient estimates as the maximum-likelihood based approach which is as expected [46]. Besides, in Mamode Khan et al [46] and Sunecher et al [47], it is proved that GQL yields more efficient estimates than CLS.…”

Section: The Inma Binma and Vinma Models Estimationmentioning

confidence: 80%

“…Brännäs and Quoreshi [16] and Quoreshi [17] have developed the inferential procedures for the INMA, BINMA and VINMA models via the CLS, FGLS and GMM approaches while Zheng et al [7] also discussed Maximum likelihood estimation for RCINAR(p)]. Mamode Khan et al [46], Sunecher et al [47], Ristic et al [31] have proposed a Generalized Quasi-likelihood (GQL) estimation technique based on the correct score specification for the BINMA(1) model only. Under these techniques, Sunecher et al [47] demonstrated through the Monte Carlo simulation BINMA(1) experiments that both CLS, GMM and GQL yield consistent parameter estimates but with GQL yielding estimates with lower bias and superior standard errors.…”

Section: Further Developmentmentioning

confidence: 99%

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A review of INMA integer-valued model class, application and further development

Shahiduzzaman¹,

Uddin²,

Mamode³

2020

Filomat

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In this paper, we review INMA time series of integer-valued model class, and discuss its further development. These models have been developed for analyzing high frequency financial count data. A vivid description of high frequency data in the context of market micro structure is given. The most distinguishing feature that makes the INMA model class different from its continuous variable MA counterpart is that multiplication of variables with real valued parameters no longer remains a viable operation when the result is to be integer-valued. In the estimation of these models, no underlying distributions are assumed. Hence, the discussion of estimations is limited to CLS, FGLS and GMM. A further development of estimation procedures for these models have also been reviewed. We suggest that the models could be estimated with Quasi Maximum Likelihood and propose in addition a Generalized Method of Moment of Quasi Maximum Likelihood. We have also discussed how INMA model class can be extended with different underlying distributions for innovations.

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Section: Discussionsupporting

confidence: 64%

Section: The Inma Binma and Vinma Models Estimationmentioning

confidence: 80%

Section: The Inma Binma and Vinma Models Estimationmentioning

confidence: 80%

Section: Further Developmentmentioning

confidence: 99%

See 2 more Smart Citations

A review of INMA integer-valued model class, application and further development

Shahiduzzaman¹,

Uddin²,

Mamode³

2020

Filomat

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“…In a recent paper by Mamode Khan et al . (), the asymptotic properties of the GQL estimators were proved. It is proved that the GQL estimators are consistent and asymptotically normal (see also Sutradhar, Jowaheer & Rao and Ristic et al .…”

Section: Introductionmentioning

confidence: 99%

A non‐stationary bivariate INAR(1) process with a simple cross‐dependence: Estimation with some properties

Bakouch

Sunecher

Khan

et al. 2020

Aus NZ J of Statistics

Self Cite

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This paper considers modelling of a non-stationary bivariate integer-valued autoregressive process of order 1 (BINAR(1)) where the cross-dependence between the counting series is formed through the relationship of the current series with the previous-lagged count series observations while the pair of innovations is independent and marginally Poisson. In addition, this paper proposes a generalised quasi-likelihood (GQL) estimating equation based on the exact specification of the mean score and the auto-covariance structure. The proposed approach is also compared with other popular techniques such as conditional maximum likelihood (CML), generalised least squares (GLS) and generalised method of moment (GMM) based on simulated data from the proposed BINAR(1). Moreover, the model is applied to weekly series of day and night road accidents arising in some regions of Mauritius and is compared with other existing BINAR(1) models.

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The Family of Bivariate Integer-Valued Auto-Regressive (BINAR) Structures and Estimation Procedures

Soobhug,

Mamode Khan,

Sunecher

2024

STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics &Amp; Health

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Investigating GQL-based inferential approaches for non-stationary BINAR(1) model under different quantum of over-dispersion with application

Cited by 6 publications

References 22 publications

A review of INMA integer-valued model class, application and further development

A review of INMA integer-valued model class, application and further development

A non‐stationary bivariate INAR(1) process with a simple cross‐dependence: Estimation with some properties

The Family of Bivariate Integer-Valued Auto-Regressive (BINAR) Structures and Estimation Procedures

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