Document Type : Original Paper
Authors
Department of Statistics, Faculty of Mathematical Sciences and Computer Shahid Chamran University of Ahvaz, Ahvaz, Islamic Republic of Iran
Abstract
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.
Keywords
- : α-fold zero modified geometric
- Binomial thinning
- Count time series
- Delaporte distribution
- INAR (1) models
Main Subjects
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