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Negative Binomial Autoregressive Process

Author

Listed:
  • Christian Gouriéroux

    () (University of Toronto; Toulouse School of Economics; CREST)

  • Yang Lu

    () (University of Paris 13; Department of Economics (CEPN))

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

  • Christian Gouriéroux & Yang Lu, 2018. "Negative Binomial Autoregressive Process," Working Papers 2018-03, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2018-03
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    4. Richard Blundell & Rachel Griffith & John van Reenen, 1999. "Market Share, Market Value and Innovation in a Panel of British Manufacturing Firms," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 529-554.
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    More about this item

    Keywords

    Negative Binomial Process; Autoregressive Gamma; Poisson-Gamma Conjugacy; Intensity; Compound Autoregressive Process; Common Factor; Pairwise Analysis; Health Insurance;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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