Fractional approaches for the distribution of innovation sequence of INAR(1) processes |
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Authors: | Josemar Rodrigues Manoel Santos-Neto N. Balakrishnan |
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Affiliation: | 1. Departamento de Matemática Aplicada e Estatística, Universidade de S?o Paulo, S?o Carlos, Brazil;2. Departamento de Estatística, Universidade Federal de Campina Grande, Campina Grande, Brazil;3. Departamento de Estatística, Universidade Federal de S?o Carlos, S?o Carlos, Brazil;4. Department of Mathematics and Statistics, McMaster University, Ontario, Canada |
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Abstract: | AbstractIn this paper, we present a fractional decomposition of the probability generating function of the innovation process of the first-order non-negative integer-valued autoregressive [INAR(1)] process to obtain the corresponding probability mass function. We also provide a comprehensive review of integer-valued time series models, based on the concept of thinning operators with geometric-type marginals. In particular, we develop two fractional approaches to obtain the distribution of innovation processes of the INAR(1) model and show that the distribution of the innovations sequence has geometric-type distribution. These approaches are discussed in detail and illustrated through a few examples. |
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Keywords: | Count data fractional decomposition geometric-type distribution innovation process time series |
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