Negative Binomial Quasi‐Likelihood Inference for General Integer‐Valued Time Series Models |
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| Authors: | Abdelhakim Aknouche Sara Bendjeddou Nassim Touche |
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| Affiliation: | 1. Faculty of Mathematics, University of Science and Technology Houari Boumediene, Algiers, Algeria;2. Mathematics Department, Qassim University, Buraydah, Saudi Arabia;3. Department of Operational Research, Faculty of Exact Sciences, University of Bejaia, Bejaia, Algeria |
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| Abstract: | Two negative binomial quasi‐maximum likelihood estimates (NB‐QMLEs) 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‐QMLEs 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‐valued GARCH model and the INAR(1) model. Application to a real dataset is given. |
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| Keywords: | Integer‐valued time series models integer‐valued GARCH integer‐valued AR geometric QMLE profile negative binomial QMLE two‐stage negative binomial QMLE Poisson QMLE consistency and asymptotic normality |
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