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Title: On periodic branching processes with immigration Authors:  Marton Ispany - University of Debrecen (Hungary) [presenting]
Abstract: Recently, there has been considerable interest in integer-valued time series models for analyzing data sets which consist of counts of events, objects or individuals. Several integer-valued time series models proposed in the literature are based on the branching model. However, these models do not account the periodic characteristic observed in some real series. We consider a branching process with immigration (BPI) in time varying environment where the environment of the process is periodic of period $S$, i.e., the mean and variance functions of the offspring and immigration distributions are periodic function with period $S$. We can interpret the process as the size of a population, e.g., the number of traffic accidents, hospital admissions, attacks on computer systems, transactions in transaction processing systems. A classification theorem is proved for periodic BPIs. Statistical properties of the process such as mean, variance, autocovariance function and marginal distributions are discussed. Moment-based conditional least squares and conditional maximum likelihood estimates of the parameters are presented for the subcritical and critical cases, respectively. Numerical estimation procedures are proposed and their performances are investigated through Monte Carlo simulations.