(University of Debrecen, Hungary)
Title — Poisson INAR processes with serial and seasonal correlation
Abstract — Recently, there has been considerable interest in integer-valued time series models. Motivation to include discrete data models comes from the need to account for the discrete nature of certain data sets, often counts of events, objects or individuals. Among the most successful integer-valued time series models proposed in the literature we mention the INteger-valued AutoRegressive model of order p (INAR(p)). However, seasonal count processes have not been investigated yet, except one of our new papers. In the talk, we study INAR processes which possess serial and seasonal structure as well. The main properties of the models will be derived such as the stationarity and the autocorrelation function. The conditional least squares and conditional maximum likelihood estimators of the model parameters will be studied and their asymptotical properties will be established. In addition, we would like to discuss the case in which the marginal distributions are Poisson in detail. Monte Carlo experiments will be conducted to evaluate and compare the performance of various estimators for finite sample sizes. Real data set on the area of insurance will be applied to evaluate the model performance.
Biography — Márton Ispány received the M.Sc.(1989) and PhD (summa cum laude) in Statistics (1997) from University of Debrecen. Since 2007 he has been with the Department of Information Technology, Faculty of Informatics, University of Debrecen. Since 2012 he has been the head of the department. Márton Ispány 's recent research interests are in branching processes (functional limit theorems, asymptotics for conditional least squares estimation, integer valued autoregression), statistical modelling(generalized SVD, contaminated statistical models, EM algorithm), data mining (decision trees, stochastic algorithms, MCMC, web mining), and applied statistics: econometrics and insurance, cross-country modelling, statistical genetics.