Estimating the parameters of a BINMA Poisson model for a non-stationary bivariate time series

Sunecher, Yuvraj; Khan, Naushad Mamode; Jowaheer, Vandna

doi:10.1080/03610918.2016.1212068

Cited by 17 publications

(17 citation statements)

References 12 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: 63%

“…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: 91%

“…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%

“…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. However, at this stage, the performance of the GQL approach has not yet been investigated on the VINMA, long memory and INARFIMA models.…”

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: 63%

Section: The Inma Binma and Vinma Models Estimationmentioning

confidence: 91%

Section: Further Developmentmentioning

confidence: 99%

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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“…Another model was proposed by [19] which extends the univariate INMA model of [18]. Recently, [15,16,24] proposed stationary and non-stationary BINMA models based on the binomial thinning operation and where the innovation series follow the bivariate Poisson distribution under timevarying moment assumptions and constant cross-correlations and used generalized quasi-likelihood estimation method.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Models, Statistics and Their Applications

2019

Springer Proceedings in Mathematics &Amp; Statistics

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A new first-order integer-valued moving average, INMA(1), model based on the negative binomial thinning operation defined by Ristić et al. [21] is proposed and characterized. It is shown that this model has negative binomial (NB) marginal distribution when the innovations follow a NB distribution and therefore it can be used in situations where the data present overdispersion. Additionally, this model is extended to the bivariate context. The Generalized Method of Moments (GMM) is used to estimate the unknown parameters of the proposed models and the results of a simulation study that intends to investigate the performance of the method show that, in general, the estimates are consistent and symmetric. Finally, the proposed model is fitted to a real dataset and the quality of the adjustment is evaluated.

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