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Negative Binomial Autoregressive Process with Stochastic Intensity
Author(s) -
Gouriéroux Christian,
Lu Yang
Publication year - 2019
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12441
Subject(s) - autoregressive model , mathematics , univariate , bivariate analysis , setar , negative binomial distribution , econometrics , statistics , estimator , star model , wishart distribution , autoregressive integrated moving average , multivariate statistics , time series , poisson distribution
We introduce negative binomial‐60 autoregressive (NBAR) processes with stochastic intensity for (univariate and bivariate) count processes. 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 formulae 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.