Fractional approaches for the distribution of innovation sequence of INAR(1) processes. Issue 9 (2nd May 2020)

• Record Type: Journal Article
• Authors: Rodrigues, Josemar; Bourguignon, Marcelo; Santos-Neto, Manoel; Balakrishnan, N.
• Is Part Of: Communications in statistics. Volume 49:Issue 9(2020)
• Page Start: 2205
• Page End: 2216
• Publication Date: 2020-05-02
• Subjects: Count data -- fractional decomposition -- geometric-type distribution -- innovation process -- time series; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1568492
• Languages: English
• ISSNs: 0361-0926

Abstract

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.