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Negative Binomial Quasi†Likelihood Inference for General Integer†Valued Time Series Models

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  • Abdelhakim Aknouche
  • Sara Bendjeddou
  • Nassim Touche

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.

Suggested Citation

  • Abdelhakim Aknouche & Sara Bendjeddou & Nassim Touche, 2018. "Negative Binomial Quasi†Likelihood Inference for General Integer†Valued Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 192-211, March.
    • Handle: RePEc:bla:jtsera:v:39:y:2018:i:2:p:192-211
    DOI: 10.1111/jtsa.12277
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    Cited by:

    1. Mamadou Lamine Diop & William Kengne, 2022. "Poisson QMLE for change-point detection in general integer-valued time series models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 373-403, April.
    2. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    3. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2020. "Forecasting transaction counts with integer-valued GARCH models," MPRA Paper 101779, University Library of Munich, Germany, revised 11 Jul 2020.
    4. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    5. Aknouche, Abdelhakim & Francq, Christian, 2023. "Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    7. Mamadou Lamine Diop & William Kengne, 2023. "A general procedure for change-point detection in multivariate time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 1-33, March.
    8. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos & Touche, Nassim, 2019. "Integer-valued stochastic volatility," MPRA Paper 91962, University Library of Munich, Germany, revised 04 Feb 2019.
    9. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2021. "Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series," MPRA Paper 110954, University Library of Munich, Germany, revised 06 Dec 2021.
    10. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2024. "Volatility models versus intensity models: analogy and differences," MPRA Paper 122528, University Library of Munich, Germany.
    11. Aknouche, Abdelhakim & Scotto, Manuel, 2022. "A multiplicative thinning-based integer-valued GARCH model," MPRA Paper 112475, University Library of Munich, Germany.
    12. Aknouche, Abdelhakim, 2024. "Periodically homogeneous Markov chains: The discrete state space case," MPRA Paper 122287, University Library of Munich, Germany.

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