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

Wagner Barreto-Souza (), Sokol Ndreca (), Rodrigo B. Silva () and Roger W. C. Silva ()
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Wagner Barreto-Souza: University College Dublin
Sokol Ndreca: Universidade Federal de Minas Gerais
Rodrigo B. Silva: Universidade Federal da Paraíba
Roger W. C. Silva: Universidade Federal de Minas Gerais

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 2, No 14, 695-725

Abstract: Abstract 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.

Keywords: Autocorrelation; Count time series; Estimation; INAR processes; Geometric thinning operator; 62M10; 60J10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-023-00849-y

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