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Title: Generalized Poisson difference autoregressive processes Authors:  Giulia Carallo - Ca' Foscari University of Venice (Italy) [presenting]
Roberto Casarin - University Ca' Foscari of Venice (Italy)
Christian Robert - Universite Paris-Dauphine (France)
Abstract: In many real-world applications, time series of counts are commonly observed given the discrete nature of the variables of interest. A new stochastic process with values in the set Z of integers with sign is introduced. The increments of the process are generalized Poisson differences and the dynamics has an autoregressive structure. In order to deal with the time-varying nature of the parameters, we introduce an integer-valued GARCH process. We study the properties of the process and exploit the thinning representation to derive stationarity conditions and distribution of the process. We develop a Bayesian inference and an efficient posterior approximation procedure based on Markov chain Monte Carlo, that allow us to make more tractable the likelihood function of the GPD and to include in the estimation prior information about the parameters. Numerical illustrations on both simulated and real data show the effectiveness of the proposed inference.