Negative Binomial Autoregressive Process

Christian Gourieroux and Yang Lu

No 2018-03, Working Papers from Center for Research in Economics and Statistics

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: Negative Binomial Process; Autoregressive Gamma; Poisson-Gamma Conjugacy; Intensity; Compound Autoregressive Process; Common Factor; Pairwise Analysis; Health Insurance (search for similar items in EconPapers)
JEL-codes: C32 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2018-03-05
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Working Paper: Negative Binomial Autoregressive Process (2018)
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