TY - JOUR ID - 85045 TI - Binomial Thinning Integer-Valued AR (1) with Poisson – α Fold Zero Modified Geometric Innovations JO - Journal of Sciences, Islamic Republic of Iran JA - JSCIENCES LA - en SN - 1016-1104 AU - Shalbaf, Maryam AU - Parham, Gholamali AU - Chinipardaz, Rahim AD - Department of Statistics, Faculty of Mathematical Sciences and Computer Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran Y1 - 2022 PY - 2022 VL - 33 IS - 1 SP - 55 EP - 63 KW - : α-fold zero modified geometric KW - Binomial thinning KW - Count time series KW - Delaporte distribution KW - INAR (1) models DO - 10.22059/jsciences.2021.320996.1007633 N2 - Real count data time series often show the phenomenon of the overdispersion. In this paper, we introduce the first-order integer-valued autoregressive process. The univariate marginal distribution is derived from the Delaporte distribution and the innovations are convolution of Poisson with -fold zero modified geometric distribution, based on binomial thinning operator, for modelling integer-valued time series with overdispersion. Some properties of the model are derived. The methods of Yule–Walker, conditional lea st squares and conditional maximum likelihood are used for estimating of the parameters, and their asymptotic properties are established. The Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. The model is fitted to time series of the weekly number of syphilis cases that are overdispersed count data. UR - https://jsciences.ut.ac.ir/article_85045.html L1 - https://jsciences.ut.ac.ir/article_85045_a175ba5fb13de8cefe8d71ba3e51a979.pdf ER -