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Periodic INAR(1) Models with Skellam-Distributed Innovations

  • Cláudia SantosEmail author
  • Isabel Pereira
  • Manuel Scotto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11621)

Abstract

In this paper, an integer-valued autoregressive model of order one (INAR(1)) with time-varying parameters and driven by a periodic sequence of innovations is introduced. The proposed INAR(1) model is based on the signed thinning operator defined by Kachour and Truquet (2011) and conveniently adapted to the periodic case. Basic notations and definitions concerning the periodic signed thinning operator are provided. Based on this thinning operator, Chesneau and Kachour (2012) established a signed INAR(1) model. Motivated by the work of Chesneau and Kachour (2012), we introduce a periodic model, denoted by S-PINAR(1), with period s. In contrast to conventional INAR(1) models, these models are defined in \(\mathbb {Z}\) allowing for negative values both for the series and its autocorrelation function. For a proper \(\mathbb {Z}\)-valued time series, a distribution for the innovation term defined on \(\mathbb {Z}\) is required. The S-PINAR(1) model assumes a specific innovation distribution, the Skellam distribution. Regarding parameter estimation, two methods are considered: conditional least squares and conditional maximum likelihood. The performance of the S-PINAR(1) model is assessed through a simulation study.

Keywords

Integer-valued autoregressive models Signed thinning operator Skellam distribution 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Coimbra College of AgriculturePolytechnic Institute of CoimbraCoimbraPortugal
  2. 2.CIDMAUniversity of AveiroAveiroPortugal
  3. 3.CEMAT and ISTUniversity of LisbonLisbonPortugal

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