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

Zezhun Chen, Angelos Dassios, George Tzougas

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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.

Original languageEnglish
JournalJournal of Applied Statistics
Early online date1 Nov 2021
DOIs
Publication statusE-pub ahead of print - 1 Nov 2021

Keywords

  • binomial-mixed Poisson INAR(1) models
  • Count data time series
  • maximum likelihood estimation
  • mixed Poisson distribution
  • overdispersion

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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