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

Zezhun Chen1, Angelos Dassios1, George Tzougas1

  • 1Department of Statistics, London School of Economics, London, UK.

Journal of Applied Statistics
|January 26, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new binomial-mixed Poisson INAR(1) model to analyze serially dependent count data. The model effectively captures overdispersion and offers flexibility in transition probabilities for various applications.

Keywords:
Count data time seriesbinomial-mixed Poisson INAR(1) modelsmaximum likelihood estimationmixed Poisson distributionoverdispersion

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Classical Poisson INAR(1) models assume independent innovations, limiting their applicability to serially dependent count data.
  • Extended Poisson INAR(1) models allow for serial dependence in innovations but may not fully capture complex data features.

Purpose of the Study:

  • To develop a novel binomial-mixed Poisson INAR(1) (BMP INAR(1)) process.
  • To extend the capabilities of INAR(1) models by incorporating a mixed Poisson component for innovations.
  • To address overdispersion and serial dependence in count time series data.

Main Methods:

  • Introduction of a mixed Poisson component into the innovations of the Poisson INAR(1) process.
  • Analysis of statistical properties, stationarity conditions, and transition probabilities for various mixing densities (e.g., Exponential, Lindley).
  • Derivation of the maximum likelihood estimation (MLE) method and its asymptotic properties.

Main Results:

  • The proposed BMP INAR(1) model accommodates a wide range of INAR(1) processes with varying transition probabilities.
  • The model effectively captures overdispersion while maintaining serial dependence in innovations.
  • The MLE method and its asymptotic properties are established for the BMP INAR(1) model.

Conclusions:

  • The BMP INAR(1) model provides a flexible and powerful tool for analyzing count time series data with overdispersion and serial dependence.
  • The model's utility is demonstrated through an application to real-world iceberg count data from a financial system.
  • This research contributes a new class of INAR(1) models with enhanced capabilities for statistical modeling.