Non-linear INAR(1) processes under an alternative geometric thinning operator

• Wagner Barreto-Souza ^[1] ; Sokol Ndreca ^[2] ; Rodrigo B. Silva ^[3] ; Roger W. C. Silva ^[2]
  1. [1] University College Dublin

     University College Dublin

     Irlanda

     
  2. [2] Universidade Federal de Minas Gerais

     Universidade Federal de Minas Gerais

     Brasil

     
  3. [3] Universidade Federal da Paraíba

     Universidade Federal da Paraíba

     Brasil

     

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 32, Nº. 2, 2023, págs. 695-725
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We propose a novel class of first-order integer-valued AutoRegressive (INAR(1)) models based on a new operator, the so-called geometric thinning operator, which induces a certain non-linearity to the models. We show that this non-linearity can produce better results in terms of prediction when compared to the linear case commonly considered in the literature. The new models are named non-linear INAR(1) (in short NonLINAR(1)) processes. We explore both stationary and non-stationary versions of the NonLINAR processes. Inference on the model parameters is addressed and the finite-sample behavior of the estimators investigated through Monte Carlo simulations. Two real data sets are analyzed to illustrate the stationary and non-stationary cases and the gain of the non-linearity induced for our method over the existing linear methods. A generalization of the geometric thinning operator and an associated NonLINAR process are also proposed and motivated for dealing with zero-inflated or zero-deflated count time series data.