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Negative binomial quasi-likelihood inference for general integer-valued time series models

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  • Aknouche, Abdelhakim
  • Bendjeddou, Sara

Abstract

Two negative binomial quasi-maximum likelihood estimates (NB-QMLE's) for a general class of count time series models are proposed. The first one is the profile NB-QMLE calculated while arbitrarily fixing the dispersion parameter of the negative binomial likelihood. The second one, termed two-stage NB-QMLE, consists of four stages estimating both conditional mean and dispersion parameters. It is shown that the two estimates are consistent and asymptotically Gaussian under mild conditions. Moreover, the two-stage NB-QMLE enjoys a certain asymptotic efficiency property provided that a negative binomial link function relating the conditional mean and conditional variance is specified. The proposed NB-QMLE's are compared with the Poisson QMLE asymptotically and in finite samples for various well-known particular classes of count time series models such as the (Poisson and negative binomial) Integer GARCH model and the INAR(1) model. Applications to two real datasets are given.

Suggested Citation

  • Aknouche, Abdelhakim & Bendjeddou, Sara, 2016. "Negative binomial quasi-likelihood inference for general integer-valued time series models," MPRA Paper 76574, University Library of Munich, Germany, revised 03 Feb 2017.
    • Handle: RePEc:pra:mprapa:76574
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    References listed on IDEAS

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    More about this item

    Keywords

    Integer-valued time series models; Integer GARCH; Integer AR; Generalized Linear Models; Quasi-likelihood; Geometric QMLE; Negative Binomial QMLE; Poisson QMLE; consistency and asymptotic normality.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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