A first order binomial mixed poisson integer-valued autoregressive model with serially dependent innovations

Zezhun Chen Chen, Angelos Dassios and George Tzougas

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of the mixed Poisson component, the model includes a large class of INAR(1) processes with different transition probabilities. Moreover, it can capture some overdispersion features coming from the data while keeping the innovations serially dependent. We discuss its statistical properties, stationarity conditions and transition probabilities for different mixing densities (Exponential, Lindley). Then, we derive the maximum likelihood estimation method and its asymptotic properties for this model. Finally, we demonstrate our approach using a real data example of iceberg count data from a financial system.

Keywords: count data time series; binomial-mixed Poisson INAR(1) models; mixed Poisson distribution; overdispersion; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2023-01-25
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Published in Journal of Applied Statistics, 25, January, 2023, 50(2), pp. 352 - 369. ISSN: 0266-4763

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:112222

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