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Fractional approaches for the distribution of innovation sequence of INAR(1) processes

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  • Josemar Rodrigues
  • Marcelo Bourguignon
  • Manoel Santos-Neto
  • N. Balakrishnan

Abstract

In 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.

Suggested Citation

  • Josemar Rodrigues & Marcelo Bourguignon & Manoel Santos-Neto & N. Balakrishnan, 2020. "Fractional approaches for the distribution of innovation sequence of INAR(1) processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(9), pages 2205-2216, May.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:9:p:2205-2216
    DOI: 10.1080/03610926.2019.1568492
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