Negative Binomial Autoregressive Process

Yang Lu () and Christian Gourieroux
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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 - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Compound Autoregressive; Poisson-gamma conjugacy (search for similar items in EconPapers)
Date: 2018-03-12
Note: View the original document on HAL open archive server: https://hal.science/hal-01730050v1
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