Tobit INARMA models for count time series with negative autocorrelation

• Christian H. Weiß ^[1] ; Hee-Young Kim ^[2] ; Fukang Zhu ^[3]
  1. [1] Helmut Schmidt University

     Helmut Schmidt University

     Hamburg, Freie und Hansestadt, Alemania

     
  2. [2] Korea University

     Korea University

     Corea del Sur

     
  3. [3] Jilin University

     Jilin University

     China

     

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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. 35, Nº. 1, 2026, págs. 117-156
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Thinning-operator-based integer-valued autoregressive moving-average (INARMA) models are quite popular for stationary count time series, the two main cases of which are the purely autoregressive INAR and purely moving-average INMA model. Like the ordinary ARMA models, the INARMA models have a linear conditional mean such that the classical Yule–Walker equations for the autocorrelation function (acf) hold. But a known drawback is that the dependence parameters have to be nonnegative such that also the resulting acf can only take nonnegative values. Modeling count time series with negative acf values in a simple construction is a long-standing open problem that has not been satisfactorily resolved so far. To address this problem, we propose two simple and flexible frameworks based on the Tobit modeling approach: Tobit INAR and Tobit INMA models. Stochastic properties, approximate linearity of the conditional mean, maximum likelihood and approximate estimation for the model parameters, and related simulations for both kinds of models are given. Two real-world data examples about a chemical process and beer sales are analyzed in detail, and it is shown that the proposed model outperforms existing ones. Extensions of the Tobit INAR model to zero-inflated counts as well as to bounded counts are also discussed.