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12 mars 2018
- handle: 10670/1.nfovan
- hal: hal-01730050
info:eu-repo/semantics/OpenAccess
Mots-clés
Compound Autoregressive Poisson-gamma conjugacy C - Mathematical and Quantitative Methods/C.C3 - Multiple or Simultaneous Equation Models • Multiple Variables/C.C3.C32 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes • State Space ModelsSujets proches
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Yang Lu et al., « Negative Binomial Autoregressive Process », HALSHS : archive ouverte en Sciences de l’Homme et de la Société, ID : 10670/1.nfovan
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Résumé
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.