The Negative Binomial INAR(1) Process under Different Thinning Processes: Can We Separate between the Different Models?

Dimitris Karlis (), Naushad Mamode Khan and Yuvraj Sunecher
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Dimitris Karlis: Department of Statistics, Athens University of Economics and Business, 10434 Athens, Greece
Naushad Mamode Khan: Department of Economics and Statistics, University of Mauritius, Reduit 80835, Mauritius
Yuvraj Sunecher: Department of Economics and Statistics, University of Mauritius, Reduit 80835, Mauritius

Stats, 2024, vol. 7, issue 3, 1-15

Abstract: The literature on discrete valued time series is expanding very fast. Very often we see new models with very similar properties to the existing ones. A natural question that arises is whether the multitude of models with very similar properties can really have a practical purpose or if they mostly present theoretical interest. In the present paper, we consider four models that have negative binomial marginal distributions and are autoregressive in order 1 behavior, but they have a very different generating mechanism. Then we try to answer the question whether we can distinguish between them with real data. Extensive simulations show that while the differences are small, we still can discriminate between the models with relatively moderate sample sizes. However, the mean forecasts are expected to be almost identical for all models.

Keywords: random thinning; iterated thinning; negative binomial thinning; INAR models (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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