Extended Poisson INAR(1) processes with equidispersion,underdispersion and overdispersion |
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Authors: | Marcelo Bourguignon Josemar Rodrigues Manoel Santos-Neto |
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Affiliation: | 1. Department of Statistics, Federal University of Rio Grande do Norte, Natal, Brazil;2. Department of Mathematics and Statistics, University of S?o Paulo, S?o Carlos, Brazil;3. Department of Statistics, Federal University of S?o Carlos, S?o Carlos, Brazil;4. Department of Statistics, Federal University of Campina Grande, Campina Grande, Brazil |
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Abstract: | Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial thinning, for modeling integer-valued time series with equidispersion, underdispersion, and overdispersion. The main properties of the models are derived. The methods of conditional maximum likelihood, Yule–Walker, and conditional least squares are used for estimating the parameters, and their asymptotic properties are established. We also use a test based on our processes for checking if the count time series considered is overdispersed or underdispersed. The proposed models are fitted to time series of the weekly number of syphilis cases and monthly counts of family violence illustrating its capabilities in challenging the overdispersed and underdispersed count data. |
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Keywords: | Double Poisson distribution generalized Poisson distribution http://www.w3.org/1998/Math/MathML" xmlns:xsi=" http://www.w3.org/2001/XMLSchema-instance" xmlns:oasis=" http://docs.oasis-open.org/ns/oasis-exchange/table" >INAR(1) process overdispersion underdispersion |
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