IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-01730050.html

Negative Binomial Autoregressive Process

Author

Listed:
  • Yang Lu

    (CEPN - Centre d'Economie de l'Université Paris Nord - UP13 - Université Paris 13 - USPC - Université Sorbonne Paris Cité - CNRS - Centre National de la Recherche Scientifique)

  • Christian Gourieroux

    (University of Toronto, TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We introduce Negative Binomial Autoregressive (NBAR) processes for (univariate and bivariate) count time series. The univariate NBAR process is defined jointly with an underlying intensity process, which is autoregressive gamma. The resulting count process is Markov, with negative binomial conditional and marginal distributions. The process is then extended to the bivariate case with a Wishart autoregressive matrix intensity process. The NBAR processes are Compound Autoregressive, which allows for simple stationarity condition and quasi-closed form nonlinear forecasting formulas at any horizon, as well as a computationally tractable generalized method of moment estimator. The model is applied to a pairwise analysis of weekly occurrence counts of a contagious disease between the greater Paris region and other French regions.

Suggested Citation

  • Yang Lu & Christian Gourieroux, 2018. "Negative Binomial Autoregressive Process," Working Papers hal-01730050, HAL.
    • Handle: RePEc:hal:wpaper:hal-01730050
    Note: View the original document on HAL open archive server: https://hal.science/hal-01730050v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01730050v1/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    2. Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
    3. Bockenholt, Ulf, 1998. "Mixed INAR(1) Poisson regression models: Analyzing heterogeneity and serial dependencies in longitudinal count data," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 317-338, November.
    4. Gourieroux, C. & Jasiak, J., 2004. "Heterogeneous INAR(1) model with application to car insurance," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 177-192, April.
    5. Richard Blundell & Rachel Griffith & John van Reenen, 1999. "Market Share, Market Value and Innovation in a Panel of British Manufacturing Firms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 529-554.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Darolles, Serge & Fol, Gaëlle Le & Lu, Yang & Sun, Ran, 2019. "Bivariate integer-autoregressive process with an application to mutual fund flows," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 181-203.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang Lu & Christian Gourieroux, 2018. "Negative Binomial Autoregressive Process," CEPN Working Papers 2018-01, Centre d'Economie de l'Université de Paris Nord.
    2. repec:hal:cepnwp:hal-01730050 is not listed on IDEAS
    3. Darolles, Serge & Fol, Gaëlle Le & Lu, Yang & Sun, Ran, 2019. "Bivariate integer-autoregressive process with an application to mutual fund flows," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 181-203.
    4. Yang Lu, 2021. "The predictive distributions of thinning‐based count processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 42-67, March.
    5. Matteo Iacopini & Carlo R.M.A. Santagiustina, 2021. "Filtering the intensity of public concern from social media count data with jumps," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1283-1302, October.
    6. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    7. Gagliardini, Patrick & Gouriéroux, Christian, 2013. "Correlated risks vs contagion in stochastic transition models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2241-2269.
    8. Liliana Meza-González & Jaime Marie Sepulveda, 2019. "The impact of competition with China in the US market on innovation in Mexican manufacturing firms," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 28(1), pages 1-21, December.
    9. Alhassan Abdul-Wakeel Karakara & Evans Osabuohien, 2020. "ICT adoption, competition and innovation of informal firms in West Africa: a comparative study of Ghana and Nigeria," Journal of Enterprising Communities: People and Places in the Global Economy, Emerald Group Publishing Limited, vol. 14(3), pages 397-414, June.
    10. Su, Hsin-Ning & Moaniba, Igam M., 2017. "Investigating the dynamics of interdisciplinary evolution in technology developments," Technological Forecasting and Social Change, Elsevier, vol. 122(C), pages 12-23.
    11. Patrick Gagliardini & Christian Gouriéroux, 2011. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 237-280, Spring.
    12. Hussinger, Katrin & Pellens, Maikel, 2019. "Guilt by association: How scientific misconduct harms prior collaborators," Research Policy, Elsevier, vol. 48(2), pages 516-530.
    13. Yu-Shan Chen & Ke-Chiun Chang, 2009. "Using neural network to analyze the influence of the patent performance upon the market value of the US pharmaceutical companies," Scientometrics, Springer;Akadémiai Kiadó, vol. 80(3), pages 637-655, September.
    14. Barge-Gil, Andrés & López, Alberto, 2014. "R&D determinants: Accounting for the differences between research and development," Research Policy, Elsevier, vol. 43(9), pages 1634-1648.
    15. Pierpaolo Parrotta & Dario Pozzoli & Mariola Pytlikova, 2014. "The nexus between labor diversity and firm’s innovation," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(2), pages 303-364, April.
    16. Bruno Amable & Jean-Bernard Chatelain & Kirsten Ralf, 2004. ""Deep Pockets": Research and Development Persistence and Economic Growth," Money Macro and Finance (MMF) Research Group Conference 2004 47, Money Macro and Finance Research Group, revised 13 Oct 2004.
    17. Aghion, Philippe & Akcigit, Ufuk & Howitt, Peter, 2014. "What Do We Learn From Schumpeterian Growth Theory?," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 0, pages 515-563, Elsevier.
    18. H. T. Tran & E. Santarelli, 2013. "Determinants and Effects of Innovative Activities in Vietnam. A Firm-level Analysis," Working Papers wp909, Dipartimento Scienze Economiche, Universita' di Bologna.
    19. J-L Hu & C-Y Fang, 2010. "Do market share and efficiency matter for each other? An application of the zero-sum gains data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 647-657, April.
    20. André Dumas TSAMBOU & Zié Ballo & Simplice A. Asongu, 2026. "Adoption of Technological and Non-technological Innovation in Manufacturing and Service Firms," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 17(2), pages 5910-5944, April.
    21. Michael Reksulak & William F. Shughart & Robert D. Tollison, 2008. "Innovation and the opportunity cost of monopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 29(8), pages 619-627.

    More about this item

    Keywords

    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-01730050. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.